library(ggplot2)
library(psych)
library(hexbin)
library(GGally)
library(tidyverse)
library(effectsize)
library(MVA)
library(MASS)
library(reshape2)
library(gridExtra)
library(grid)
library(car)
library(robustbase)
library(MVN)
library(ICSNP)
library(mvdalab)
library(rstatix)
library(heplots)

EXPLORATORY DATA ANALYSIS

set.seed(467)
data=read.csv("C:/Users/ASUS/Desktop/stat467project/Life-Expectancy-Data-Updated.csv")
data["Region"]=as.factor(data$Region)
data["Country"]=as.factor(data$Country)
data2=subset(data, select = -c(Economy_status_Developed,Economy_status_Developing))
data3=subset(data, select = c(Economy_status_Developed,Economy_status_Developing))
data=cbind(data2, 
      Economy_status = apply(data3, 1, 
                    function(x) names(x)[as.logical(as.numeric(
                      as.character(x)))]))
data["Economy_status"]=as.factor(data$Economy_status)
data["Hepatitis_B"]=as.numeric(data$Hepatitis_B)
data["Measles"]=as.numeric(data$Measles)
data["Polio"]=as.numeric(data$Polio)
data["Diphtheria"]=as.numeric(data$Diphtheria)
data["GDP_per_capita"]=as.numeric(data$GDP_per_capita)
data <- data[data["Year"]==2015, ]
data=subset(data,select = -Year)
data=na.omit(data)
str(data)
## 'data.frame':    179 obs. of  19 variables:
##  $ Country                    : Factor w/ 179 levels "Afghanistan",..: 165 149 134 30 61 3 123 98 122 176 ...
##  $ Region                     : Factor w/ 9 levels "Africa","Asia",..: 5 4 8 1 1 1 5 1 8 2 ...
##  $ Infant_deaths              : num  11.1 2.7 6.6 57 39.7 21.6 9.6 41.3 2.2 17.4 ...
##  $ Under_five_deaths          : num  13 3.3 8.2 88 59.8 25.2 11.2 59 2.7 21.8 ...
##  $ Adult_mortality            : num  105.8 57.9 223 340.1 261.7 ...
##  $ Alcohol_consumption        : num  1.32 10.35 8.06 4.55 2.69 ...
##  $ Hepatitis_B                : num  97 97 97 84 97 95 99 69 88 97 ...
##  $ Measles                    : num  65 94 97 64 64 99 98 64 91 65 ...
##  $ BMI                        : num  27.8 26 26.2 24.3 23.9 25.5 26.3 21.3 26.6 21.7 ...
##  $ Polio                      : num  97 97 97 77 96 95 99 68 95 97 ...
##  $ Diphtheria                 : num  97 97 97 84 97 95 99 69 95 97 ...
##  $ Incidents_HIV              : num  0.08 0.09 0.08 1.12 0.96 0.05 0.05 0.24 0.04 0.12 ...
##  $ GDP_per_capita             : num  11006 25742 9313 1383 661 ...
##  $ Population_mln             : num  78.53 46.44 144.1 23.3 2.09 ...
##  $ Thinness_ten_nineteen_years: num  4.9 0.6 2.3 5.6 7.3 6 7.1 7.1 0.8 14.2 ...
##  $ Thinness_five_nine_years   : num  4.8 0.5 2.3 5.5 7.2 5.8 6.9 7.1 0.7 14.5 ...
##  $ Schooling                  : num  7.8 9.7 12 6.1 3.4 7.9 9.5 6.1 12.5 8 ...
##  $ Life_expectancy            : num  76.5 82.8 71.2 57.6 60.9 76.1 76.9 65.5 82.3 75.1 ...
##  $ Economy_status             : Factor w/ 2 levels "Economy_status_Developed",..: 2 1 2 2 2 2 2 2 1 2 ...
summary(data)
##                 Country                              Region   Infant_deaths  
##  Afghanistan        :  1   Africa                       :51   Min.   : 1.80  
##  Albania            :  1   Asia                         :27   1st Qu.: 6.65  
##  Algeria            :  1   European Union               :27   Median :15.20  
##  Angola             :  1   Central America and Caribbean:19   Mean   :23.56  
##  Antigua and Barbuda:  1   Rest of Europe               :15   3rd Qu.:36.55  
##  Argentina          :  1   Middle East                  :14   Max.   :95.10  
##  (Other)            :173   (Other)                      :26                  
##  Under_five_deaths Adult_mortality  Alcohol_consumption  Hepatitis_B  
##  Min.   :  2.30    Min.   : 49.38   Min.   : 0.000      Min.   :22.0  
##  1st Qu.:  7.85    1st Qu.: 90.79   1st Qu.: 1.360      1st Qu.:82.5  
##  Median : 17.50    Median :146.52   Median : 4.040      Median :92.0  
##  Mean   : 31.68    Mean   :163.67   Mean   : 4.729      Mean   :87.1  
##  3rd Qu.: 49.95    3rd Qu.:215.65   3rd Qu.: 7.760      3rd Qu.:97.0  
##  Max.   :140.20    Max.   :513.48   Max.   :16.720      Max.   :99.0  
##                                                                       
##     Measles           BMI           Polio         Diphtheria   
##  Min.   :21.00   Min.   :20.5   Min.   :37.00   Min.   :16.00  
##  1st Qu.:64.00   1st Qu.:23.8   1st Qu.:85.00   1st Qu.:85.50  
##  Median :84.00   Median :26.2   Median :93.00   Median :93.00  
##  Mean   :80.23   Mean   :25.6   Mean   :88.26   Mean   :87.92  
##  3rd Qu.:94.00   3rd Qu.:27.0   3rd Qu.:97.00   3rd Qu.:97.00  
##  Max.   :99.00   Max.   :32.1   Max.   :99.00   Max.   :99.00  
##                                                                
##  Incidents_HIV     GDP_per_capita   Population_mln    
##  Min.   : 0.0100   Min.   :   306   Min.   :   0.090  
##  1st Qu.: 0.0800   1st Qu.:  1690   1st Qu.:   2.215  
##  Median : 0.1400   Median :  5391   Median :   9.110  
##  Mean   : 0.6098   Mean   : 12617   Mean   :  40.088  
##  3rd Qu.: 0.3700   3rd Qu.: 14274   3rd Qu.:  27.445  
##  Max.   :14.3000   Max.   :105462   Max.   :1379.860  
##                                                       
##  Thinness_ten_nineteen_years Thinness_five_nine_years   Schooling     
##  Min.   : 0.10               Min.   : 0.100           Min.   : 1.400  
##  1st Qu.: 1.50               1st Qu.: 1.500           1st Qu.: 5.950  
##  Median : 3.50               Median : 3.400           Median : 8.700  
##  Mean   : 4.55               Mean   : 4.594           Mean   : 8.361  
##  3rd Qu.: 6.50               3rd Qu.: 6.450           3rd Qu.:11.050  
##  Max.   :26.70               Max.   :27.300           Max.   :14.100  
##                                                                       
##  Life_expectancy                   Economy_status
##  Min.   :50.90   Economy_status_Developed : 37   
##  1st Qu.:66.30   Economy_status_Developing:142   
##  Median :73.00                                   
##  Mean   :71.46                                   
##  3rd Qu.:76.85                                   
##  Max.   :83.80                                   
## 
head(data)
##               Country         Region Infant_deaths Under_five_deaths
## 1             Turkiye    Middle East          11.1              13.0
## 2               Spain European Union           2.7               3.3
## 7  Russian Federation Rest of Europe           6.6               8.2
## 28           Cameroon         Africa          57.0              88.0
## 44        Gambia, The         Africa          39.7              59.8
## 58            Algeria         Africa          21.6              25.2
##    Adult_mortality Alcohol_consumption Hepatitis_B Measles  BMI Polio
## 1         105.8240                1.32          97      65 27.8    97
## 2          57.9025               10.35          97      94 26.0    97
## 7         223.0000                8.06          97      97 26.2    97
## 28        340.1265                4.55          84      64 24.3    77
## 44        261.7065                2.69          97      64 23.9    96
## 58         95.8155                0.55          95      99 25.5    95
##    Diphtheria Incidents_HIV GDP_per_capita Population_mln
## 1          97          0.08          11006          78.53
## 2          97          0.09          25742          46.44
## 7          97          0.08           9313         144.10
## 28         84          1.12           1383          23.30
## 44         97          0.96            661           2.09
## 58         95          0.05           4178          39.73
##    Thinness_ten_nineteen_years Thinness_five_nine_years Schooling
## 1                          4.9                      4.8       7.8
## 2                          0.6                      0.5       9.7
## 7                          2.3                      2.3      12.0
## 28                         5.6                      5.5       6.1
## 44                         7.3                      7.2       3.4
## 58                         6.0                      5.8       7.9
##    Life_expectancy            Economy_status
## 1             76.5 Economy_status_Developing
## 2             82.8  Economy_status_Developed
## 7             71.2 Economy_status_Developing
## 28            57.6 Economy_status_Developing
## 44            60.9 Economy_status_Developing
## 58            76.1 Economy_status_Developing
data2=subset(data,select = -c(Region,Country,Economy_status))
cormat <- round(cor(data2),2)
get_upper_tri <- function(cormat){
  cormat[lower.tri(cormat)]<- NA
  return(cormat)
  }
reorder_cormat <- function(cormat){
# Use correlation between variables as distance
dd <- as.dist((1-cormat)/2)
hc <- hclust(dd)
cormat <-cormat[hc$order, hc$order]
}
cormat <- reorder_cormat(cormat)
upper_tri <- get_upper_tri(cormat)
melted_cormat <- melt(upper_tri, na.rm = TRUE)
ggplot(melted_cormat, aes(Var2, Var1, fill = value))+
 geom_tile(color = "white")+
 scale_fill_gradient2(low = "blue", high = "red", mid = "white", 
   midpoint = 0, limit = c(-1,1), space = "Lab", 
    name="Pearson\nCorrelation") +
  theme_minimal()+ # minimal theme
 theme(axis.text.x = element_text(angle = 45, vjust = 1, 
    size = 12, hjust = 1))+
 coord_fixed()+ 
geom_text(aes(Var2, Var1, label = value), color = "black", size = 3) +
theme(
  axis.text.x=element_blank(),
  axis.title.x = element_blank(),
  axis.title.y = element_blank(),
  panel.grid.major = element_blank(),
  panel.border = element_blank(),
  panel.background = element_blank(),
  axis.ticks = element_blank(),
  legend.justification = c(1, 0),
  legend.position = c(0.6, 0.7),
  legend.direction = "horizontal")+
  guides(fill = guide_colorbar(barwidth = 7, barheight = 1,
                title.position = "top", title.hjust = 0.5))

mvn(data2,multivariatePlot= "qq")$plot

## NULL

The variables which violates the multivariate normality since there are large deviations from the line

result <- mvn(data = data2, mvnTest = "royston")
result$multivariateNormality
##      Test        H      p value MVN
## 1 Royston 342.1765 2.013471e-70  NO

Since p-value is smaller than 0.05, we can reject the null hypthosis which is that the data follows normal distribution

qqplots = lapply(1:ncol(data2), function(.x) ggplot(data2,aes(sample=as.numeric(unlist(data2[,.x]))))+stat_qq()+stat_qq_line()+ theme_classic() +ggtitle(colnames(data2)[.x]))
require(gridExtra)
do.call(grid.arrange,  qqplots)

hplots = lapply(1:ncol(data2), function(.x) ggplot(data2,aes(x=unlist(data2[,colnames(data2)[.x]])))+geom_histogram(aes(y=..density..), colour="black", fill="white")+geom_density(alpha=.5, fill="darkblue")+ theme_classic()+labs(x=colnames(data2)[.x])+ggtitle(colnames(data2)[.x]))
require(gridExtra)
do.call(grid.arrange,  hplots)

As you see, the variables which violates the multivariate normality.

# create univariate histograms
result <- mvn(data = data2, mvnTest = "royston", univariateTest = "SW" )
result$univariateNormality 
##            Test                    Variable Statistic   p value Normality
## 1  Shapiro-Wilk        Infant_deaths           0.8612  <0.001      NO    
## 2  Shapiro-Wilk      Under_five_deaths         0.8187  <0.001      NO    
## 3  Shapiro-Wilk       Adult_mortality          0.9202  <0.001      NO    
## 4  Shapiro-Wilk     Alcohol_consumption        0.9335  <0.001      NO    
## 5  Shapiro-Wilk         Hepatitis_B            0.7746  <0.001      NO    
## 6  Shapiro-Wilk           Measles              0.8876  <0.001      NO    
## 7  Shapiro-Wilk             BMI                0.9698   6e-04      NO    
## 8  Shapiro-Wilk            Polio               0.7744  <0.001      NO    
## 9  Shapiro-Wilk         Diphtheria             0.7283  <0.001      NO    
## 10 Shapiro-Wilk        Incidents_HIV           0.3677  <0.001      NO    
## 11 Shapiro-Wilk       GDP_per_capita           0.6862  <0.001      NO    
## 12 Shapiro-Wilk       Population_mln           0.2339  <0.001      NO    
## 13 Shapiro-Wilk Thinness_ten_nineteen_years    0.8216  <0.001      NO    
## 14 Shapiro-Wilk  Thinness_five_nine_years      0.8242  <0.001      NO    
## 15 Shapiro-Wilk          Schooling             0.9617   1e-04      NO    
## 16 Shapiro-Wilk       Life_expectancy          0.9528  <0.001      NO

Since the all p-values are smaller than 0.05, the variables which violates the multivariate normality.

result$Descriptives
##                               n         Mean      Std.Dev    Median     Min
## Infant_deaths               179 2.355866e+01    21.487508   15.2000   1.800
## Under_five_deaths           179 3.168045e+01    32.217096   17.5000   2.300
## Adult_mortality             179 1.636676e+02    89.954470  146.5195  49.384
## Alcohol_consumption         179 4.728994e+00     3.743322    4.0400   0.000
## Hepatitis_B                 179 8.710056e+01    14.167575   92.0000  22.000
## Measles                     179 8.022905e+01    16.185999   84.0000  21.000
## BMI                         179 2.559609e+01     2.191669   26.2000  20.500
## Polio                       179 8.826257e+01    13.024320   93.0000  37.000
## Diphtheria                  179 8.791620e+01    14.693831   93.0000  16.000
## Incidents_HIV               179 6.097765e-01     1.621318    0.1400   0.010
## GDP_per_capita              179 1.261730e+04 17719.612926 5391.0000 306.000
## Population_mln              179 4.008793e+01   146.506422    9.1100   0.090
## Thinness_ten_nineteen_years 179 4.549721e+00     4.115992    3.5000   0.100
## Thinness_five_nine_years    179 4.593855e+00     4.195546    3.4000   0.100
## Schooling                   179 8.360894e+00     3.146986    8.7000   1.400
## Life_expectancy             179 7.146369e+01     7.832270   73.0000  50.900
##                                     Max       25th       75th        Skew
## Infant_deaths                   95.1000    6.65000    36.5500  1.12850717
## Under_five_deaths              140.2000    7.85000    49.9500  1.35663447
## Adult_mortality                513.4755   90.78575   215.6492  1.04384225
## Alcohol_consumption             16.7200    1.36000     7.7600  0.48900835
## Hepatitis_B                     99.0000   82.50000    97.0000 -1.88604401
## Measles                         99.0000   64.00000    94.0000 -0.84526412
## BMI                             32.1000   23.80000    27.0000 -0.08139383
## Polio                           99.0000   85.00000    97.0000 -1.79562345
## Diphtheria                      99.0000   85.50000    97.0000 -2.19634211
## Incidents_HIV                   14.3000    0.08000     0.3700  5.32064829
## GDP_per_capita              105462.0000 1690.00000 14274.5000  2.30984461
## Population_mln                1379.8600    2.21500    27.4450  7.98900304
## Thinness_ten_nineteen_years     26.7000    1.50000     6.5000  1.91176983
## Thinness_five_nine_years        27.3000    1.50000     6.4500  1.92769092
## Schooling                       14.1000    5.95000    11.0500 -0.27144789
## Life_expectancy                 83.8000   66.30000    76.8500 -0.59113627
##                               Kurtosis
## Infant_deaths                0.4568213
## Under_five_deaths            1.0935217
## Adult_mortality              0.9966979
## Alcohol_consumption         -0.6896498
## Hepatitis_B                  3.6237679
## Measles                      0.3260768
## BMI                         -0.1759413
## Polio                        2.9408103
## Diphtheria                   5.4145578
## Incidents_HIV               34.3579078
## GDP_per_capita               5.8912927
## Population_mln              67.7536827
## Thinness_ten_nineteen_years  5.3396564
## Thinness_five_nine_years     5.4675130
## Schooling                   -1.0221789
## Life_expectancy             -0.4306512
Bivariate<-matrix(rep(0,36),(ncol(data2)*(ncol(data2)-1)),3)
for (i in 1:(ncol(data2)-1)){
  for (j in (i+1):ncol(data2)){
  Bivariate[(i*j),1:2]<-names(data2[,c(i,j)])
  Bivariate[(i*j),3]<-mvn(data = data2[,c(i,j)], mvnTest = "royston", univariateTest = "SW")$multivariateNormality[,4]
  }}
for(i in 1:nrow(Bivariate)){
  if(Bivariate[i,3]=="0"){
    Bivariate[i,3]=NA
  }
}
Bivariate=na.omit(Bivariate)
Bivariate
##       [,1]                          [,2]                          [,3]
##  [1,] "Infant_deaths"               "Under_five_deaths"           "NO"
##  [2,] "Infant_deaths"               "Adult_mortality"             "NO"
##  [3,] "Infant_deaths"               "Alcohol_consumption"         "NO"
##  [4,] "Infant_deaths"               "Hepatitis_B"                 "NO"
##  [5,] "Under_five_deaths"           "Adult_mortality"             "NO"
##  [6,] "Infant_deaths"               "BMI"                         "NO"
##  [7,] "Under_five_deaths"           "Alcohol_consumption"         "NO"
##  [8,] "Infant_deaths"               "Diphtheria"                  "NO"
##  [9,] "Under_five_deaths"           "Hepatitis_B"                 "NO"
## [10,] "Infant_deaths"               "GDP_per_capita"              "NO"
## [11,] "Adult_mortality"             "Alcohol_consumption"         "NO"
## [12,] "Infant_deaths"               "Thinness_ten_nineteen_years" "NO"
## [13,] "Under_five_deaths"           "BMI"                         "NO"
## [14,] "Adult_mortality"             "Hepatitis_B"                 "NO"
## [15,] "Under_five_deaths"           "Polio"                       "NO"
## [16,] "Adult_mortality"             "Measles"                     "NO"
## [17,] "Alcohol_consumption"         "Hepatitis_B"                 "NO"
## [18,] "Adult_mortality"             "BMI"                         "NO"
## [19,] "Under_five_deaths"           "GDP_per_capita"              "NO"
## [20,] "Alcohol_consumption"         "Measles"                     "NO"
## [21,] "Under_five_deaths"           "Thinness_ten_nineteen_years" "NO"
## [22,] "Adult_mortality"             "Diphtheria"                  "NO"
## [23,] "Alcohol_consumption"         "BMI"                         "NO"
## [24,] "Hepatitis_B"                 "Measles"                     "NO"
## [25,] "Alcohol_consumption"         "Polio"                       "NO"
## [26,] "Adult_mortality"             "GDP_per_capita"              "NO"
## [27,] "Hepatitis_B"                 "BMI"                         "NO"
## [28,] "Alcohol_consumption"         "Diphtheria"                  "NO"
## [29,] "Adult_mortality"             "Thinness_ten_nineteen_years" "NO"
## [30,] "Hepatitis_B"                 "Polio"                       "NO"
## [31,] "Measles"                     "BMI"                         "NO"
## [32,] "Alcohol_consumption"         "GDP_per_capita"              "NO"
## [33,] "Hepatitis_B"                 "Diphtheria"                  "NO"
## [34,] "Measles"                     "Polio"                       "NO"
## [35,] "Hepatitis_B"                 "Incidents_HIV"               "NO"
## [36,] "Alcohol_consumption"         "Thinness_ten_nineteen_years" "NO"
## [37,] "Measles"                     "Diphtheria"                  "NO"
## [38,] "Hepatitis_B"                 "GDP_per_capita"              "NO"
## [39,] "BMI"                         "Polio"                       "NO"
## [40,] "Measles"                     "Incidents_HIV"               "NO"
## [41,] "BMI"                         "Diphtheria"                  "NO"
## [42,] "Alcohol_consumption"         "Life_expectancy"             "NO"
## [43,] "Hepatitis_B"                 "Thinness_ten_nineteen_years" "NO"
## [44,] "Measles"                     "GDP_per_capita"              "NO"
## [45,] "BMI"                         "Incidents_HIV"               "NO"
## [46,] "Polio"                       "Diphtheria"                  "NO"
## [47,] "Hepatitis_B"                 "Schooling"                   "NO"
## [48,] "BMI"                         "GDP_per_capita"              "NO"
## [49,] "Measles"                     "Thinness_ten_nineteen_years" "NO"
## [50,] "Polio"                       "Incidents_HIV"               "NO"
## [51,] "BMI"                         "Population_mln"              "NO"
## [52,] "Polio"                       "GDP_per_capita"              "NO"
## [53,] "Diphtheria"                  "Incidents_HIV"               "NO"
## [54,] "BMI"                         "Thinness_ten_nineteen_years" "NO"
## [55,] "Polio"                       "Population_mln"              "NO"
## [56,] "BMI"                         "Thinness_five_nine_years"    "NO"
## [57,] "Diphtheria"                  "GDP_per_capita"              "NO"
## [58,] "Polio"                       "Thinness_ten_nineteen_years" "NO"
## [59,] "BMI"                         "Schooling"                   "NO"
## [60,] "Diphtheria"                  "Population_mln"              "NO"
## [61,] "Incidents_HIV"               "GDP_per_capita"              "NO"
## [62,] "Polio"                       "Thinness_five_nine_years"    "NO"
## [63,] "Diphtheria"                  "Thinness_ten_nineteen_years" "NO"
## [64,] "Incidents_HIV"               "Population_mln"              "NO"
## [65,] "Diphtheria"                  "Thinness_five_nine_years"    "NO"
## [66,] "Polio"                       "Life_expectancy"             "NO"
## [67,] "Incidents_HIV"               "Thinness_ten_nineteen_years" "NO"
## [68,] "GDP_per_capita"              "Population_mln"              "NO"
## [69,] "Diphtheria"                  "Schooling"                   "NO"
## [70,] "Incidents_HIV"               "Thinness_five_nine_years"    "NO"
## [71,] "GDP_per_capita"              "Thinness_ten_nineteen_years" "NO"
## [72,] "Diphtheria"                  "Life_expectancy"             "NO"
## [73,] "Incidents_HIV"               "Schooling"                   "NO"
## [74,] "GDP_per_capita"              "Thinness_five_nine_years"    "NO"
## [75,] "Population_mln"              "Thinness_ten_nineteen_years" "NO"
## [76,] "Incidents_HIV"               "Life_expectancy"             "NO"
## [77,] "GDP_per_capita"              "Schooling"                   "NO"
## [78,] "Population_mln"              "Thinness_five_nine_years"    "NO"
## [79,] "GDP_per_capita"              "Life_expectancy"             "NO"
## [80,] "Population_mln"              "Schooling"                   "NO"
## [81,] "Thinness_ten_nineteen_years" "Thinness_five_nine_years"    "NO"
## [82,] "Population_mln"              "Life_expectancy"             "NO"
## [83,] "Thinness_ten_nineteen_years" "Schooling"                   "NO"
## [84,] "Thinness_ten_nineteen_years" "Life_expectancy"             "NO"
## [85,] "Thinness_five_nine_years"    "Schooling"                   "NO"
## [86,] "Thinness_five_nine_years"    "Life_expectancy"             "NO"
## [87,] "Schooling"                   "Life_expectancy"             "NO"
## attr(,"na.action")
##   [1]   1  17  19  23  25  29  31  34  37  38  41  43  46  47  49  51  53  57
##  [19]  58  59  61  62  67  68  69  71  73  74  76  79  81  82  83  85  86  87
##  [37]  89  92  93  94  95  97 100 101 102 103 106 107 109 111 113 114 115 116
##  [55] 118 119 121 122 123 124 125 127 129 131 133 134 136 137 138 139 141 142
##  [73] 145 146 147 148 149 151 152 153 155 157 158 159 161 162 163 164 166 167
##  [91] 169 170 171 172 173 174 175 177 178 179 181 183 184 185 186 187 188 189
## [109] 190 191 193 194 196 197 198 199 200 201 202 203 204 205 206 207 209 211
## [127] 212 213 214 215 216 217 218 219 220 221 222 223 225 226 227 228 229 230
## [145] 231 232 233 234 235 236 237 238 239
## attr(,"class")
## [1] "omit"

In addition to the univarite non-normality of every variable, bivariate non-normality also exhibits non-normality.

result <- mvn(data = data2, mvnTest = "royston", multivariateOutlierMethod = "quan")

As can be seen, this dataset contains 84 outlier observations that are proved by the Mahalanobis Distance.

result <- mvn(data = data2, mvnTest = "royston", multivariateOutlierMethod = "adj")

As can be seen, this dataset contains 80 outlier observations that are proved by the Adjusted Mahalanobis Distance.

One Population Mean

datatest=data[,c("Thinness_five_nine_years","Thinness_ten_nineteen_years")]
mu0=c(4.5,4.5)
xbar = colMeans(datatest)
test<-mvn(datatest,mvnTest = "mardia")
test$multivariateNormality
##              Test        Statistic p value Result
## 1 Mardia Skewness 2455.21532300756       0     NO
## 2 Mardia Kurtosis  138.82062093672       0     NO
## 3             MVN             <NA>    <NA>     NO
test<-mvn(datatest,mvnTest = "mardia", univariateTest = "SW")
test$univariateNormality
##           Test                    Variable Statistic   p value Normality
## 1 Shapiro-Wilk  Thinness_five_nine_years      0.8242  <0.001      NO    
## 2 Shapiro-Wilk Thinness_ten_nineteen_years    0.8216  <0.001      NO
a=1
for(i in colnames(datatest)){
  if(any(data[,i]<=0)){
    next
  }
  else{
    b <- boxcox(lm(as.numeric(unlist(datatest[,i]))~ 1))
    lambda=b$x[which.max(b$y)]}
    datatest[i] <- (as.numeric(unlist(datatest[,i]))^ lambda - 1) / lambda
    mu0[a]=(mu0[a]^lambda-1)/lambda
    a=a+1
  }

test<-mvn(datatest,mvnTest = "mardia", univariateTest = "SW")
test$univariateNormality
##           Test                    Variable Statistic   p value Normality
## 1 Shapiro-Wilk  Thinness_five_nine_years      0.9879    0.1280    YES   
## 2 Shapiro-Wilk Thinness_ten_nineteen_years    0.9859    0.0701    YES

The normality is satisfied. Let’s see our response matrix before we begin the formal tests.

error.bars (datatest, ylab="Group Means", xlab=" Dependent Variables")

mu0
## [1] 1.785949 1.785949
TF9 <- lm(Thinness_five_nine_years ~ 1, data = datatest)
confint(TF9)
##               2.5 %   97.5 %
## (Intercept) 1.18284 1.562754
TF19 <- lm(Thinness_ten_nineteen_years ~ 1, data = datatest)
confint(TF19)
##                2.5 %   97.5 %
## (Intercept) 1.194447 1.562957

As we have seen, the both CI do not include the mu0.

HotellingsT2(datatest,mu=mu0)
## 
##  Hotelling's one sample T2-test
## 
## data:  datatest
## T.2 = 9.4836, df1 = 2, df2 = 177, p-value = 0.0001223
## alternative hypothesis: true location is not equal to c(1.78594895730098,1.78594895730098)

Since p-value is smaller than 0.05, we reject H0. Therefore, we don’t have enough evidence to conclude that the transformation of the mean vector equals to transformation of (4.5,4.5).

MVcis(datatest)

##                                 [,1]     [,2]
## Thinness_five_nine_years    1.134499 1.611095
## Thinness_ten_nineteen_years 1.147557 1.609847

mu0 values do not appear in the simultaneous confidence intervals for each variable because they do not fall inside the confidence region (that is, the point does not appear inside the ellipse), we reject the null hypothesis.

Two Independent Samples

datatest[,"Economy_status"]=data[,"Economy_status"]
datatest %>% group_by(Economy_status) %>%  shapiro_test(Thinness_five_nine_years
,Thinness_ten_nineteen_years)
## # A tibble: 4 × 4
##   Economy_status            variable                    statistic       p
##   <fct>                     <chr>                           <dbl>   <dbl>
## 1 Economy_status_Developed  Thinness_five_nine_years        0.977 0.625  
## 2 Economy_status_Developed  Thinness_ten_nineteen_years     0.973 0.501  
## 3 Economy_status_Developing Thinness_five_nine_years        0.972 0.00493
## 4 Economy_status_Developing Thinness_ten_nineteen_years     0.974 0.00839
datanondev=datatest[datatest["Economy_status"]=="Economy_status_Developing",c(1,2)]
qqplots = lapply(1:ncol(datanondev), function(.x)
  ggplot(datanondev,aes(sample=as.numeric(unlist(datanondev[,.x]))))+stat_qq()+stat_qq_line()+ theme_classic() +ggtitle(colnames(datanondev)[.x]))
require(gridExtra)
do.call(grid.arrange,  qqplots)

# create univariate histograms
result <- mvn(data = datanondev, mvnTest = "royston", univariatePlot = "histogram", univariateTest = "SW" )

Although the p-value is significant for each combination of Economy_status_Developing, we can not reject null hypothesis because of visual inspection leading us to believe that the data is normal.

boxM(Y = cbind(datatest$Thinness_five_nine_years    ,datatest$Thinness_ten_nineteen_years), group = factor(datatest$Economy_status))
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  cbind(datatest$Thinness_five_nine_years, datatest$Thinness_ten_nineteen_years)
## Chi-Sq (approx.) = 86.822, df = 3, p-value < 2.2e-16

We reject the null hypothesis and come to the conclusion that variance-covariance matrices are not equal for every combination of the dependent variable created by each group in the independent variable since the p-value for Box’s M test is significant.

Given that the assumption is false, it would be wise to use Levene’s test to verify the homogeneity of variance assumption and determine which variable fails in equal variance.

leveneTest(Thinness_five_nine_years ~ Economy_status, datatest)
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value   Pr(>F)   
## group   1  10.126 0.001727 **
##       177                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(Thinness_ten_nineteen_years ~ Economy_status, datatest)
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1  14.493 0.0001937 ***
##       177                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

According to Levene’s tests, both variable fail in equal variance.

HotellingsT2(cbind(datatest$Thinness_ten_nineteen_years,datatest$Thinness_five_nine_years) ~ datatest$Economy_status)
## 
##  Hotelling's two sample T2-test
## 
## data:  cbind(datatest$Thinness_ten_nineteen_years, datatest$Thinness_five_nine_years) by datatest$Economy_status
## T.2 = 38.137, df1 = 2, df2 = 176, p-value = 1.732e-14
## alternative hypothesis: true location difference is not equal to c(0,0)

We reject H0 since the p value is significant. As a result, we have sufficient evidence to prove that the economy has an impact on the mean of the responses.


#Simultaneous Confidence Intervals
xbar_0<-colMeans(datatest[datatest["Economy_status"]=="Economy_status_Developing",c(1,2)])
xbar_1<-colMeans(datatest[datatest["Economy_status"]=="Economy_status_Developed",c(1,2)])

n1<-dim(datatest[datatest["Economy_status"]=="Economy_status_Developing",])[1]
n2<-dim(datatest[datatest["Economy_status"]=="Economy_status_Developed",])[1]

p<-2
F<-qf(0.05, p, (n1+n2-p-1), lower.tail=FALSE)

c_square<-(((n1+n2-2)*p)/(n1+n2-p-1))*F

sd1<-sd(datatest$Thinness_five_nine_years)
sd2<-sd(datatest$Thinness_ten_nineteen_years)

LC1<-(xbar_0[1]-xbar_1[1])-sqrt(c_square)*sqrt((1/n1)+(1/n2))*sd1
UC1<-(xbar_0[1]-xbar_1[1])+sqrt(c_square)*sqrt((1/n1)+(1/n2))*sd1

SCI_1<-c(LC1, UC1)

LC2<-(xbar_0[2]-xbar_1[2])-sqrt(c_square)*sqrt((1/n1)+(1/n2))*sd1
UC2<-(xbar_0[2]-xbar_1[2])+sqrt(c_square)*sqrt((1/n1)+(1/n2))*sd1

SCI_2<-c(LC2, UC2)

#Bonferroni Confidence Intervals
m<-2
t<-qt(0.05/2*m, n1+n2-2, lower.tail=FALSE)

LC1<-(xbar_0[1]-xbar_1[1])-t*sqrt((1/n1)+(1/n2))*sd2
UC1<-(xbar_0[1]-xbar_1[1])+t*sqrt((1/n1)+(1/n2))*sd2

BCI_1<-c(LC1, UC1)

LC2<-(xbar_0[2]-xbar_1[2])-t*sqrt((1/n1)+(1/n2))*sd2
UC2<-(xbar_0[2]-xbar_1[2])+t*sqrt((1/n1)+(1/n2))*sd2

BCI_2<-c(LC2, UC2)


SCI_1 
## Thinness_five_nine_years Thinness_five_nine_years 
##                 1.155275                 2.332301
BCI_1 
## Thinness_five_nine_years Thinness_five_nine_years 
##                 1.362527                 2.125050
SCI_2 
## Thinness_ten_nineteen_years Thinness_ten_nineteen_years 
##                    1.051640                    2.228666
BCI_2 
## Thinness_ten_nineteen_years Thinness_ten_nineteen_years 
##                    1.258891                    2.021414

Bonferroni confidence intervals give narrower intervals and both CI for Thinness_ten_nineteen_years and Thinness_five_nine_years.However, any of them does not include 0.

One Way MANOVA

dataowa=datatest[,c("Thinness_five_nine_years","Thinness_ten_nineteen_years")]
dataowa["Region"]=data[,"Region"]
dataowa
##      Thinness_five_nine_years Thinness_ten_nineteen_years
## 1                  1.87675095                  1.90603667
## 2                 -0.64240208                 -0.48289863
## 7                  0.91497527                  0.91497527
## 28                 2.07260535                  2.09897556
## 44                 2.47799809                  2.49941974
## 58                 2.15063600                  2.20092896
## 75                 2.41231344                  2.45634377
## 102                2.45634377                  2.45634377
## 111               -0.34290589                 -0.21770132
## 113                3.65256541                  3.61477701
## 122                1.65724882                  1.62355500
## 161                2.22558793                  2.29772543
## 167                0.80660548                  0.86174855
## 174                3.84441782                  3.79789609
## 183                2.88636810                  2.92137584
## 203                0.74938068                  0.68988528
## 217                2.68260955                  2.70198297
## 220                0.96643138                  0.91497527
## 242                0.56318021                  0.56318021
## 269                0.09632668                  0.18606541
## 272               -1.05636402                 -0.82902522
## 301                2.72117568                  2.74019149
## 304                0.18606541                  0.09632668
## 331                1.96324071                  2.01872570
## 334                2.43445091                  2.45634377
## 416                0.80660548                  0.80660548
## 427                2.49941974                  2.49941974
## 444                0.34937100                  0.42429321
## 452                0.18606541                  0.34937100
## 474                1.32730923                  1.36729377
## 488                0.42429321                  0.42429321
## 496                0.62790224                  0.62790224
## 499                2.38992500                  2.41231344
## 512                1.40634675                  1.44451632
## 547               -1.80232087                 -1.80232087
## 557                1.06453417                  1.11139871
## 559                2.01872570                  2.07260535
## 580                1.20121770                  1.48184688
## 585                2.68260955                  2.72117568
## 591                1.40634675                  1.44451632
## 599               -0.64240208                 -0.48289863
## 609                1.55415190                  1.55415190
## 627                0.27016343                  0.18606541
## 629                2.01872570                  2.07260535
## 639                2.56234400                  2.60322806
## 640                4.88339003                  4.83716463
## 651                1.06453417                  1.06453417
## 688                1.36729377                  1.36729377
## 697                1.36729377                  1.36729377
## 700                2.24993446                  2.29772543
## 717                3.45711218                  3.42974412
## 728                2.20092896                  2.12498202
## 733               -0.10413666                  0.00000000
## 741                2.47799809                  2.49941974
## 764                1.44451632                  1.48184688
## 766                0.62790224                  0.68988528
## 770                2.49941974                  2.52061436
## 787                2.22558793                  2.27397746
## 810                0.42429321                  0.49542577
## 811                0.62790224                  0.68988528
## 833                1.62355500                  1.62355500
## 838                2.32118654                  2.36727900
## 840                2.17594824                  2.22558793
## 850                1.20121770                  1.15693209
## 852                2.95581497                  2.97282781
## 853                2.58288928                  2.58288928
## 869                0.91497527                  0.86174855
## 874               -0.64240208                 -0.34290589
## 901                3.53729759                  3.53729759
## 903                2.32118654                  2.36727900
## 904                2.17594824                  2.12498202
## 907                1.96324071                  2.01872570
## 957                2.09897556                  2.09897556
## 1000               2.01872570                  2.07260535
## 1011               4.21727064                  4.17741892
## 1058               2.22558793                  2.24993446
## 1064              -0.21770132                 -0.10413666
## 1067               3.97878983                  3.96787407
## 1068               1.40634675                  1.44451632
## 1117               1.90603667                  1.90603667
## 1146               0.27016343                  0.34937100
## 1150               0.56318021                  0.62790224
## 1157               0.00000000                  0.00000000
## 1158               2.70198297                  2.72117568
## 1164               1.51837942                  1.55415190
## 1197               0.62790224                  0.80660548
## 1205               0.80660548                  0.80660548
## 1206               2.24993446                  2.29772543
## 1225               0.18606541                  0.18606541
## 1227               2.88636810                  2.92137584
## 1251               1.72276330                  1.72276330
## 1262               0.68988528                  0.80660548
## 1266               1.51837942                  1.48184688
## 1306               0.80660548                  0.68988528
## 1320               1.15693209                  1.11139871
## 1338               2.45634377                  2.54158737
## 1358               2.66305150                  2.68260955
## 1481               2.07260535                  2.09897556
## 1492              -0.21770132                 -0.21770132
## 1503               2.56234400                  2.60322806
## 1531               0.62790224                  0.62790224
## 1536              -0.34290589                 -0.21770132
## 1559               0.09632668                  0.18606541
## 1566              -1.35307896                 -1.05636402
## 1588               0.34937100                  0.42429321
## 1604               1.40634675                  1.36729377
## 1614              -1.05636402                 -0.82902522
## 1620               0.18606541                  0.18606541
## 1624               1.90603667                  1.99119070
## 1629               2.54158737                  2.60322806
## 1707               3.51088038                  3.53729759
## 1710               2.22558793                  2.27397746
## 1713               1.01624602                  0.96643138
## 1716               0.74938068                  0.74938068
## 1722               0.68988528                  0.74938068
## 1732              -1.35307896                 -1.35307896
## 1785               0.91497527                  0.91497527
## 1801               1.96324071                  2.12498202
## 1810              -0.48289863                 -0.21770132
## 1820               2.90394439                  2.93866516
## 1824               0.86174855                  0.80660548
## 1844               4.08533410                  4.04327328
## 1875               2.29772543                  2.34436857
## 1882               1.28634070                  1.24433103
## 1905               0.34937100                  0.42429321
## 1948              -0.21770132                 -0.21770132
## 1950               0.09632668                  0.09632668
## 1976               2.29772543                  2.32118654
## 1984              -0.10413666                  0.09632668
## 1989               2.12498202                  2.12498202
## 2022               2.38992500                  2.41231344
## 2077               0.27016343                  0.27016343
## 2081               0.86174855                  0.86174855
## 2118               2.75903410                  2.74019149
## 2120               0.74938068                  0.68988528
## 2127              -0.48289863                 -0.48289863
## 2128               1.36729377                  1.44451632
## 2146               0.09632668                  0.09632668
## 2148               0.34937100                  0.42429321
## 2178               0.68988528                  0.68988528
## 2182               0.49542577                  0.49542577
## 2235               2.68260955                  2.68260955
## 2279              -0.48289863                 -0.48289863
## 2281               1.15693209                  1.15693209
## 2291               1.15693209                  1.11139871
## 2322               1.01624602                  1.01624602
## 2324               1.44451632                  1.44451632
## 2325              -0.10413666                  0.00000000
## 2339               2.07260535                  2.15063600
## 2357              -0.48289863                 -0.21770132
## 2368              -0.10413666                  0.00000000
## 2379               3.83287241                  3.76239602
## 2396               0.00000000                  0.00000000
## 2405               2.34436857                  2.34436857
## 2410               2.81455771                  2.79621381
## 2443              -0.10413666                  0.00000000
## 2449               2.24993446                  2.32118654
## 2469               0.68988528                  0.68988528
## 2496               2.95581497                  0.00000000
## 2519               1.11139871                  1.01624602
## 2526               1.58919952                  1.58919952
## 2582               2.07260535                  2.07260535
## 2618               2.54158737                  2.64330473
## 2621               0.09632668                  0.18606541
## 2642               3.18256970                  0.68988528
## 2651               1.51837942                  1.62355500
## 2662               2.54158737                  2.58288928
## 2680              -1.80232087                 -1.35307896
## 2702               3.71421615                  3.72635394
## 2711               0.18606541                  0.34937100
## 2713              -0.48289863                 -0.34290589
## 2728               2.49941974                  2.54158737
## 2738              -1.80232087                 -1.80232087
## 2753               2.01872570                  1.75463538
## 2754               2.29772543                  2.32118654
## 2821               0.42429321                  0.49542577
## 2841               2.04585955                  2.09897556
## 2847               0.56318021                  0.62790224
## 2849               2.22558793                  2.24993446
##                             Region
## 1                      Middle East
## 2                   European Union
## 7                   Rest of Europe
## 28                          Africa
## 44                          Africa
## 58                          Africa
## 75                     Middle East
## 102                         Africa
## 111                 Rest of Europe
## 113                           Asia
## 122                         Africa
## 161                         Africa
## 167                 European Union
## 174                           Asia
## 183                         Africa
## 203                 Rest of Europe
## 217                         Africa
## 220                 Rest of Europe
## 242  Central America and Caribbean
## 269                    Middle East
## 272                        Oceania
## 301                         Africa
## 304                        Oceania
## 331                    Middle East
## 334                         Africa
## 416  Central America and Caribbean
## 427                         Africa
## 444                 European Union
## 452                           Asia
## 474  Central America and Caribbean
## 488                  North America
## 496                 European Union
## 499                         Africa
## 512  Central America and Caribbean
## 547                        Oceania
## 557                  South America
## 559                  South America
## 580                           Asia
## 585                         Africa
## 591                    Middle East
## 599                  North America
## 609  Central America and Caribbean
## 627                 Rest of Europe
## 629                         Africa
## 639                    Middle East
## 640                           Asia
## 651                 European Union
## 688                           Asia
## 697  Central America and Caribbean
## 700                         Africa
## 717                           Asia
## 728                         Africa
## 733                 European Union
## 741                         Africa
## 764                         Africa
## 766                 European Union
## 770                         Africa
## 787                    Middle East
## 810  Central America and Caribbean
## 811  Central America and Caribbean
## 833                    Middle East
## 838                         Africa
## 840                         Africa
## 850                           Asia
## 852                         Africa
## 853                           Asia
## 869                           Asia
## 874                 European Union
## 901                           Asia
## 903                         Africa
## 904  Central America and Caribbean
## 907                    Middle East
## 957                         Africa
## 1000 Central America and Caribbean
## 1011                          Asia
## 1058                        Africa
## 1064                European Union
## 1067                          Asia
## 1068 Central America and Caribbean
## 1117                   Middle East
## 1146                European Union
## 1150 Central America and Caribbean
## 1157                European Union
## 1158                        Africa
## 1164 Central America and Caribbean
## 1197                          Asia
## 1205                Rest of Europe
## 1206                        Africa
## 1225                European Union
## 1227                        Africa
## 1251 Central America and Caribbean
## 1262                 South America
## 1266                          Asia
## 1306                European Union
## 1320                Rest of Europe
## 1338                        Africa
## 1358                        Africa
## 1481                        Africa
## 1492                European Union
## 1503                        Africa
## 1531                Rest of Europe
## 1536                European Union
## 1559                 South America
## 1566                European Union
## 1588                European Union
## 1604                          Asia
## 1614                Rest of Europe
## 1620 Central America and Caribbean
## 1624                   Middle East
## 1629                        Africa
## 1707                   Middle East
## 1710                        Africa
## 1713                          Asia
## 1716                Rest of Europe
## 1722                 South America
## 1732                       Oceania
## 1785                Rest of Europe
## 1801                          Asia
## 1810                Rest of Europe
## 1820                        Africa
## 1824                Rest of Europe
## 1844                          Asia
## 1875                        Africa
## 1882                          Asia
## 1905                 South America
## 1948                 South America
## 1950                European Union
## 1976                        Africa
## 1984                European Union
## 1989                        Africa
## 2022                        Africa
## 2077                       Oceania
## 2081                          Asia
## 2118                   Middle East
## 2120                European Union
## 2127                European Union
## 2128 Central America and Caribbean
## 2146                 South America
## 2148                       Oceania
## 2178                          Asia
## 2182                European Union
## 2235                        Africa
## 2279                       Oceania
## 2281                        Africa
## 2291                Rest of Europe
## 2322 Central America and Caribbean
## 2324                 South America
## 2325                European Union
## 2339                        Africa
## 2357                 North America
## 2368                 South America
## 2379                          Asia
## 2396                European Union
## 2405                        Africa
## 2410                          Asia
## 2443                Rest of Europe
## 2449                        Africa
## 2469                European Union
## 2496                          Asia
## 2519                European Union
## 2526 Central America and Caribbean
## 2582                        Africa
## 2618                        Africa
## 2621                 South America
## 2642                       Oceania
## 2651                       Oceania
## 2662                        Africa
## 2680                       Oceania
## 2702                          Asia
## 2711                        Africa
## 2713                European Union
## 2728                          Asia
## 2738                       Oceania
## 2753                        Africa
## 2754                        Africa
## 2821                 South America
## 2841                        Africa
## 2847 Central America and Caribbean
## 2849                   Middle East
dataowa %>% group_by(Region) %>%  summarise(n = n(), 
                                               mean_9 = mean(Thinness_five_nine_years), 
                                               sd_9 = sd(Thinness_five_nine_years),
                                               mean_19 = mean(Thinness_ten_nineteen_years),
                                               sd_19 = sd(Thinness_ten_nineteen_years))
## # A tibble: 9 × 6
##   Region                            n mean_9  sd_9 mean_19 sd_19
##   <fct>                         <int>  <dbl> <dbl>   <dbl> <dbl>
## 1 Africa                           51  2.29  0.455  2.32   0.452
## 2 Asia                             27  2.38  1.38   2.28   1.42 
## 3 Central America and Caribbean    19  1.17  0.566  1.19   0.556
## 4 European Union                   27  0.131 0.589  0.191  0.516
## 5 Middle East                      14  2.03  0.764  2.07   0.750
## 6 North America                     3 -0.234 0.575 -0.0921 0.466
## 7 Oceania                          11 -0.254 1.58  -0.411  1.12 
## 8 Rest of Europe                   15  0.479 0.671  0.505  0.580
## 9 South America                    12  0.554 0.671  0.613  0.666
p1 <- ggplot(dataowa, aes(x = Region, y = Thinness_five_nine_years, fill = Region)) + geom_boxplot(outlier.shape = NA) + geom_jitter(width = 0.2) + theme(legend.position="top")+theme_minimal()+
labs(title = "The Box Plot of Thinness_five_nine_years by Region" ,subtitle = "Transformed Thinness_five_nine_years.")
p2 <- ggplot(dataowa, aes(x = Region, y = Thinness_ten_nineteen_years, fill = Region)) + geom_boxplot(outlier.shape = NA) + geom_jitter(width = 0.2) + theme(legend.position="top")+theme_minimal()+
labs(title = "The Box Plot of Thinness_ten_nineteen_years by Region" ,subtitle = "Tranformed Thinness_ten_nineteen_years.")
grid.arrange(p1, p2, ncol=2) 

dataowa %>% group_by(Region) %>%  shapiro_test(Thinness_five_nine_years,Thinness_ten_nineteen_years)
## # A tibble: 18 × 4
##    Region                        variable                    statistic         p
##    <fct>                         <chr>                           <dbl>     <dbl>
##  1 Africa                        Thinness_five_nine_years        0.811   1.33e-6
##  2 Africa                        Thinness_ten_nineteen_years     0.839   6.51e-6
##  3 Asia                          Thinness_five_nine_years        0.922   4.32e-2
##  4 Asia                          Thinness_ten_nineteen_years     0.920   3.99e-2
##  5 Central America and Caribbean Thinness_five_nine_years        0.946   3.35e-1
##  6 Central America and Caribbean Thinness_ten_nineteen_years     0.940   2.68e-1
##  7 European Union                Thinness_five_nine_years        0.973   6.92e-1
##  8 European Union                Thinness_ten_nineteen_years     0.971   6.30e-1
##  9 Middle East                   Thinness_five_nine_years        0.913   1.74e-1
## 10 Middle East                   Thinness_ten_nineteen_years     0.920   2.19e-1
## 11 North America                 Thinness_five_nine_years        0.859   2.66e-1
## 12 North America                 Thinness_ten_nineteen_years     0.946   5.51e-1
## 13 Oceania                       Thinness_five_nine_years        0.887   1.28e-1
## 14 Oceania                       Thinness_ten_nineteen_years     0.941   5.37e-1
## 15 Rest of Europe                Thinness_five_nine_years        0.847   1.58e-2
## 16 Rest of Europe                Thinness_ten_nineteen_years     0.860   2.39e-2
## 17 South America                 Thinness_five_nine_years        0.906   1.88e-1
## 18 South America                 Thinness_ten_nineteen_years     0.927   3.47e-1
dataowa2=dataowa
dataowa2 %>% group_by(Region) %>%  shapiro_test(Thinness_five_nine_years,Thinness_ten_nineteen_years)
## # A tibble: 18 × 4
##    Region                        variable                    statistic         p
##    <fct>                         <chr>                           <dbl>     <dbl>
##  1 Africa                        Thinness_five_nine_years        0.811   1.33e-6
##  2 Africa                        Thinness_ten_nineteen_years     0.839   6.51e-6
##  3 Asia                          Thinness_five_nine_years        0.922   4.32e-2
##  4 Asia                          Thinness_ten_nineteen_years     0.920   3.99e-2
##  5 Central America and Caribbean Thinness_five_nine_years        0.946   3.35e-1
##  6 Central America and Caribbean Thinness_ten_nineteen_years     0.940   2.68e-1
##  7 European Union                Thinness_five_nine_years        0.973   6.92e-1
##  8 European Union                Thinness_ten_nineteen_years     0.971   6.30e-1
##  9 Middle East                   Thinness_five_nine_years        0.913   1.74e-1
## 10 Middle East                   Thinness_ten_nineteen_years     0.920   2.19e-1
## 11 North America                 Thinness_five_nine_years        0.859   2.66e-1
## 12 North America                 Thinness_ten_nineteen_years     0.946   5.51e-1
## 13 Oceania                       Thinness_five_nine_years        0.887   1.28e-1
## 14 Oceania                       Thinness_ten_nineteen_years     0.941   5.37e-1
## 15 Rest of Europe                Thinness_five_nine_years        0.847   1.58e-2
## 16 Rest of Europe                Thinness_ten_nineteen_years     0.860   2.39e-2
## 17 South America                 Thinness_five_nine_years        0.906   1.88e-1
## 18 South America                 Thinness_ten_nineteen_years     0.927   3.47e-1
boxM(Y = cbind(dataowa2$Thinness_five_nine_years,dataowa2$Thinness_ten_nineteen_years), group = factor(dataowa2$Region))
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  cbind(dataowa2$Thinness_five_nine_years, dataowa2$Thinness_ten_nineteen_years)
## Chi-Sq (approx.) = 453.64, df = 24, p-value < 2.2e-16
leveneTest(Thinness_ten_nineteen_years ~ Region, dataowa2)
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   8   12.91 1.878e-14 ***
##       170                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
leveneTest(Thinness_five_nine_years ~ Region, dataowa2)
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   8  11.044 1.668e-12 ***
##       170                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
m1 <- manova(cbind(Thinness_five_nine_years,Thinness_ten_nineteen_years) ~ Region, data = dataowa2)
summary(m1)
##            Df  Pillai approx F num Df den Df    Pr(>F)    
## Region      8 0.67122   10.734     16    340 < 2.2e-16 ***
## Residuals 170                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary.aov(m1)
##  Response Thinness_five_nine_years :
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## Region        8 175.96 21.9951   31.35 < 2.2e-16 ***
## Residuals   170 119.27  0.7016                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Thinness_ten_nineteen_years :
##              Df Sum Sq Mean Sq F value    Pr(>F)    
## Region        8 172.66 21.5830  34.908 < 2.2e-16 ***
## Residuals   170 105.11  0.6183                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Two-Way MANOVA

datatwa=cbind(dataowa,data["Economy_status"])
datatwa
##      Thinness_five_nine_years Thinness_ten_nineteen_years
## 1                  1.87675095                  1.90603667
## 2                 -0.64240208                 -0.48289863
## 7                  0.91497527                  0.91497527
## 28                 2.07260535                  2.09897556
## 44                 2.47799809                  2.49941974
## 58                 2.15063600                  2.20092896
## 75                 2.41231344                  2.45634377
## 102                2.45634377                  2.45634377
## 111               -0.34290589                 -0.21770132
## 113                3.65256541                  3.61477701
## 122                1.65724882                  1.62355500
## 161                2.22558793                  2.29772543
## 167                0.80660548                  0.86174855
## 174                3.84441782                  3.79789609
## 183                2.88636810                  2.92137584
## 203                0.74938068                  0.68988528
## 217                2.68260955                  2.70198297
## 220                0.96643138                  0.91497527
## 242                0.56318021                  0.56318021
## 269                0.09632668                  0.18606541
## 272               -1.05636402                 -0.82902522
## 301                2.72117568                  2.74019149
## 304                0.18606541                  0.09632668
## 331                1.96324071                  2.01872570
## 334                2.43445091                  2.45634377
## 416                0.80660548                  0.80660548
## 427                2.49941974                  2.49941974
## 444                0.34937100                  0.42429321
## 452                0.18606541                  0.34937100
## 474                1.32730923                  1.36729377
## 488                0.42429321                  0.42429321
## 496                0.62790224                  0.62790224
## 499                2.38992500                  2.41231344
## 512                1.40634675                  1.44451632
## 547               -1.80232087                 -1.80232087
## 557                1.06453417                  1.11139871
## 559                2.01872570                  2.07260535
## 580                1.20121770                  1.48184688
## 585                2.68260955                  2.72117568
## 591                1.40634675                  1.44451632
## 599               -0.64240208                 -0.48289863
## 609                1.55415190                  1.55415190
## 627                0.27016343                  0.18606541
## 629                2.01872570                  2.07260535
## 639                2.56234400                  2.60322806
## 640                4.88339003                  4.83716463
## 651                1.06453417                  1.06453417
## 688                1.36729377                  1.36729377
## 697                1.36729377                  1.36729377
## 700                2.24993446                  2.29772543
## 717                3.45711218                  3.42974412
## 728                2.20092896                  2.12498202
## 733               -0.10413666                  0.00000000
## 741                2.47799809                  2.49941974
## 764                1.44451632                  1.48184688
## 766                0.62790224                  0.68988528
## 770                2.49941974                  2.52061436
## 787                2.22558793                  2.27397746
## 810                0.42429321                  0.49542577
## 811                0.62790224                  0.68988528
## 833                1.62355500                  1.62355500
## 838                2.32118654                  2.36727900
## 840                2.17594824                  2.22558793
## 850                1.20121770                  1.15693209
## 852                2.95581497                  2.97282781
## 853                2.58288928                  2.58288928
## 869                0.91497527                  0.86174855
## 874               -0.64240208                 -0.34290589
## 901                3.53729759                  3.53729759
## 903                2.32118654                  2.36727900
## 904                2.17594824                  2.12498202
## 907                1.96324071                  2.01872570
## 957                2.09897556                  2.09897556
## 1000               2.01872570                  2.07260535
## 1011               4.21727064                  4.17741892
## 1058               2.22558793                  2.24993446
## 1064              -0.21770132                 -0.10413666
## 1067               3.97878983                  3.96787407
## 1068               1.40634675                  1.44451632
## 1117               1.90603667                  1.90603667
## 1146               0.27016343                  0.34937100
## 1150               0.56318021                  0.62790224
## 1157               0.00000000                  0.00000000
## 1158               2.70198297                  2.72117568
## 1164               1.51837942                  1.55415190
## 1197               0.62790224                  0.80660548
## 1205               0.80660548                  0.80660548
## 1206               2.24993446                  2.29772543
## 1225               0.18606541                  0.18606541
## 1227               2.88636810                  2.92137584
## 1251               1.72276330                  1.72276330
## 1262               0.68988528                  0.80660548
## 1266               1.51837942                  1.48184688
## 1306               0.80660548                  0.68988528
## 1320               1.15693209                  1.11139871
## 1338               2.45634377                  2.54158737
## 1358               2.66305150                  2.68260955
## 1481               2.07260535                  2.09897556
## 1492              -0.21770132                 -0.21770132
## 1503               2.56234400                  2.60322806
## 1531               0.62790224                  0.62790224
## 1536              -0.34290589                 -0.21770132
## 1559               0.09632668                  0.18606541
## 1566              -1.35307896                 -1.05636402
## 1588               0.34937100                  0.42429321
## 1604               1.40634675                  1.36729377
## 1614              -1.05636402                 -0.82902522
## 1620               0.18606541                  0.18606541
## 1624               1.90603667                  1.99119070
## 1629               2.54158737                  2.60322806
## 1707               3.51088038                  3.53729759
## 1710               2.22558793                  2.27397746
## 1713               1.01624602                  0.96643138
## 1716               0.74938068                  0.74938068
## 1722               0.68988528                  0.74938068
## 1732              -1.35307896                 -1.35307896
## 1785               0.91497527                  0.91497527
## 1801               1.96324071                  2.12498202
## 1810              -0.48289863                 -0.21770132
## 1820               2.90394439                  2.93866516
## 1824               0.86174855                  0.80660548
## 1844               4.08533410                  4.04327328
## 1875               2.29772543                  2.34436857
## 1882               1.28634070                  1.24433103
## 1905               0.34937100                  0.42429321
## 1948              -0.21770132                 -0.21770132
## 1950               0.09632668                  0.09632668
## 1976               2.29772543                  2.32118654
## 1984              -0.10413666                  0.09632668
## 1989               2.12498202                  2.12498202
## 2022               2.38992500                  2.41231344
## 2077               0.27016343                  0.27016343
## 2081               0.86174855                  0.86174855
## 2118               2.75903410                  2.74019149
## 2120               0.74938068                  0.68988528
## 2127              -0.48289863                 -0.48289863
## 2128               1.36729377                  1.44451632
## 2146               0.09632668                  0.09632668
## 2148               0.34937100                  0.42429321
## 2178               0.68988528                  0.68988528
## 2182               0.49542577                  0.49542577
## 2235               2.68260955                  2.68260955
## 2279              -0.48289863                 -0.48289863
## 2281               1.15693209                  1.15693209
## 2291               1.15693209                  1.11139871
## 2322               1.01624602                  1.01624602
## 2324               1.44451632                  1.44451632
## 2325              -0.10413666                  0.00000000
## 2339               2.07260535                  2.15063600
## 2357              -0.48289863                 -0.21770132
## 2368              -0.10413666                  0.00000000
## 2379               3.83287241                  3.76239602
## 2396               0.00000000                  0.00000000
## 2405               2.34436857                  2.34436857
## 2410               2.81455771                  2.79621381
## 2443              -0.10413666                  0.00000000
## 2449               2.24993446                  2.32118654
## 2469               0.68988528                  0.68988528
## 2496               2.95581497                  0.00000000
## 2519               1.11139871                  1.01624602
## 2526               1.58919952                  1.58919952
## 2582               2.07260535                  2.07260535
## 2618               2.54158737                  2.64330473
## 2621               0.09632668                  0.18606541
## 2642               3.18256970                  0.68988528
## 2651               1.51837942                  1.62355500
## 2662               2.54158737                  2.58288928
## 2680              -1.80232087                 -1.35307896
## 2702               3.71421615                  3.72635394
## 2711               0.18606541                  0.34937100
## 2713              -0.48289863                 -0.34290589
## 2728               2.49941974                  2.54158737
## 2738              -1.80232087                 -1.80232087
## 2753               2.01872570                  1.75463538
## 2754               2.29772543                  2.32118654
## 2821               0.42429321                  0.49542577
## 2841               2.04585955                  2.09897556
## 2847               0.56318021                  0.62790224
## 2849               2.22558793                  2.24993446
##                             Region            Economy_status
## 1                      Middle East Economy_status_Developing
## 2                   European Union  Economy_status_Developed
## 7                   Rest of Europe Economy_status_Developing
## 28                          Africa Economy_status_Developing
## 44                          Africa Economy_status_Developing
## 58                          Africa Economy_status_Developing
## 75                     Middle East Economy_status_Developing
## 102                         Africa Economy_status_Developing
## 111                 Rest of Europe  Economy_status_Developed
## 113                           Asia Economy_status_Developing
## 122                         Africa Economy_status_Developing
## 161                         Africa Economy_status_Developing
## 167                 European Union  Economy_status_Developed
## 174                           Asia Economy_status_Developing
## 183                         Africa Economy_status_Developing
## 203                 Rest of Europe Economy_status_Developing
## 217                         Africa Economy_status_Developing
## 220                 Rest of Europe Economy_status_Developing
## 242  Central America and Caribbean Economy_status_Developing
## 269                    Middle East  Economy_status_Developed
## 272                        Oceania  Economy_status_Developed
## 301                         Africa Economy_status_Developing
## 304                        Oceania Economy_status_Developing
## 331                    Middle East Economy_status_Developing
## 334                         Africa Economy_status_Developing
## 416  Central America and Caribbean Economy_status_Developing
## 427                         Africa Economy_status_Developing
## 444                 European Union  Economy_status_Developed
## 452                           Asia Economy_status_Developing
## 474  Central America and Caribbean Economy_status_Developing
## 488                  North America Economy_status_Developing
## 496                 European Union  Economy_status_Developed
## 499                         Africa Economy_status_Developing
## 512  Central America and Caribbean Economy_status_Developing
## 547                        Oceania Economy_status_Developing
## 557                  South America Economy_status_Developing
## 559                  South America Economy_status_Developing
## 580                           Asia Economy_status_Developing
## 585                         Africa Economy_status_Developing
## 591                    Middle East Economy_status_Developing
## 599                  North America  Economy_status_Developed
## 609  Central America and Caribbean Economy_status_Developing
## 627                 Rest of Europe Economy_status_Developing
## 629                         Africa Economy_status_Developing
## 639                    Middle East Economy_status_Developing
## 640                           Asia Economy_status_Developing
## 651                 European Union  Economy_status_Developed
## 688                           Asia Economy_status_Developing
## 697  Central America and Caribbean Economy_status_Developing
## 700                         Africa Economy_status_Developing
## 717                           Asia Economy_status_Developing
## 728                         Africa Economy_status_Developing
## 733                 European Union  Economy_status_Developed
## 741                         Africa Economy_status_Developing
## 764                         Africa Economy_status_Developing
## 766                 European Union  Economy_status_Developed
## 770                         Africa Economy_status_Developing
## 787                    Middle East Economy_status_Developing
## 810  Central America and Caribbean Economy_status_Developing
## 811  Central America and Caribbean Economy_status_Developing
## 833                    Middle East Economy_status_Developing
## 838                         Africa Economy_status_Developing
## 840                         Africa Economy_status_Developing
## 850                           Asia Economy_status_Developing
## 852                         Africa Economy_status_Developing
## 853                           Asia Economy_status_Developing
## 869                           Asia Economy_status_Developing
## 874                 European Union  Economy_status_Developed
## 901                           Asia Economy_status_Developing
## 903                         Africa Economy_status_Developing
## 904  Central America and Caribbean Economy_status_Developing
## 907                    Middle East Economy_status_Developing
## 957                         Africa Economy_status_Developing
## 1000 Central America and Caribbean Economy_status_Developing
## 1011                          Asia Economy_status_Developing
## 1058                        Africa Economy_status_Developing
## 1064                European Union  Economy_status_Developed
## 1067                          Asia Economy_status_Developing
## 1068 Central America and Caribbean Economy_status_Developing
## 1117                   Middle East Economy_status_Developing
## 1146                European Union  Economy_status_Developed
## 1150 Central America and Caribbean Economy_status_Developing
## 1157                European Union  Economy_status_Developed
## 1158                        Africa Economy_status_Developing
## 1164 Central America and Caribbean Economy_status_Developing
## 1197                          Asia  Economy_status_Developed
## 1205                Rest of Europe Economy_status_Developing
## 1206                        Africa Economy_status_Developing
## 1225                European Union  Economy_status_Developed
## 1227                        Africa Economy_status_Developing
## 1251 Central America and Caribbean Economy_status_Developing
## 1262                 South America Economy_status_Developing
## 1266                          Asia Economy_status_Developing
## 1306                European Union  Economy_status_Developed
## 1320                Rest of Europe Economy_status_Developing
## 1338                        Africa Economy_status_Developing
## 1358                        Africa Economy_status_Developing
## 1481                        Africa Economy_status_Developing
## 1492                European Union  Economy_status_Developed
## 1503                        Africa Economy_status_Developing
## 1531                Rest of Europe Economy_status_Developing
## 1536                European Union  Economy_status_Developed
## 1559                 South America Economy_status_Developing
## 1566                European Union  Economy_status_Developed
## 1588                European Union  Economy_status_Developed
## 1604                          Asia Economy_status_Developing
## 1614                Rest of Europe  Economy_status_Developed
## 1620 Central America and Caribbean Economy_status_Developing
## 1624                   Middle East Economy_status_Developing
## 1629                        Africa Economy_status_Developing
## 1707                   Middle East Economy_status_Developing
## 1710                        Africa Economy_status_Developing
## 1713                          Asia Economy_status_Developing
## 1716                Rest of Europe Economy_status_Developing
## 1722                 South America Economy_status_Developing
## 1732                       Oceania Economy_status_Developing
## 1785                Rest of Europe Economy_status_Developing
## 1801                          Asia Economy_status_Developing
## 1810                Rest of Europe  Economy_status_Developed
## 1820                        Africa Economy_status_Developing
## 1824                Rest of Europe Economy_status_Developing
## 1844                          Asia Economy_status_Developing
## 1875                        Africa Economy_status_Developing
## 1882                          Asia Economy_status_Developing
## 1905                 South America Economy_status_Developing
## 1948                 South America Economy_status_Developing
## 1950                European Union  Economy_status_Developed
## 1976                        Africa Economy_status_Developing
## 1984                European Union  Economy_status_Developed
## 1989                        Africa Economy_status_Developing
## 2022                        Africa Economy_status_Developing
## 2077                       Oceania Economy_status_Developing
## 2081                          Asia Economy_status_Developing
## 2118                   Middle East Economy_status_Developing
## 2120                European Union  Economy_status_Developed
## 2127                European Union  Economy_status_Developed
## 2128 Central America and Caribbean Economy_status_Developing
## 2146                 South America Economy_status_Developing
## 2148                       Oceania Economy_status_Developing
## 2178                          Asia Economy_status_Developing
## 2182                European Union  Economy_status_Developed
## 2235                        Africa Economy_status_Developing
## 2279                       Oceania  Economy_status_Developed
## 2281                        Africa Economy_status_Developing
## 2291                Rest of Europe Economy_status_Developing
## 2322 Central America and Caribbean Economy_status_Developing
## 2324                 South America Economy_status_Developing
## 2325                European Union  Economy_status_Developed
## 2339                        Africa Economy_status_Developing
## 2357                 North America  Economy_status_Developed
## 2368                 South America Economy_status_Developing
## 2379                          Asia Economy_status_Developing
## 2396                European Union  Economy_status_Developed
## 2405                        Africa Economy_status_Developing
## 2410                          Asia Economy_status_Developing
## 2443                Rest of Europe  Economy_status_Developed
## 2449                        Africa Economy_status_Developing
## 2469                European Union  Economy_status_Developed
## 2496                          Asia Economy_status_Developing
## 2519                European Union  Economy_status_Developed
## 2526 Central America and Caribbean Economy_status_Developing
## 2582                        Africa Economy_status_Developing
## 2618                        Africa Economy_status_Developing
## 2621                 South America Economy_status_Developing
## 2642                       Oceania Economy_status_Developing
## 2651                       Oceania Economy_status_Developing
## 2662                        Africa Economy_status_Developing
## 2680                       Oceania Economy_status_Developing
## 2702                          Asia Economy_status_Developing
## 2711                        Africa Economy_status_Developing
## 2713                European Union  Economy_status_Developed
## 2728                          Asia Economy_status_Developing
## 2738                       Oceania Economy_status_Developing
## 2753                        Africa Economy_status_Developing
## 2754                        Africa Economy_status_Developing
## 2821                 South America Economy_status_Developing
## 2841                        Africa Economy_status_Developing
## 2847 Central America and Caribbean Economy_status_Developing
## 2849                   Middle East Economy_status_Developing
datatwa2=datatwa
datatwa2$mix<-as.factor(paste(datatwa$Region,datatwa$Economy_status))
datatwa2 %>% group_by(mix) %>% summarise(n = n()) 
## # A tibble: 14 × 2
##    mix                                                         n
##    <fct>                                                   <int>
##  1 Africa Economy_status_Developing                           51
##  2 Asia Economy_status_Developed                               1
##  3 Asia Economy_status_Developing                             26
##  4 Central America and Caribbean Economy_status_Developing    19
##  5 European Union Economy_status_Developed                    27
##  6 Middle East Economy_status_Developed                        1
##  7 Middle East Economy_status_Developing                      13
##  8 North America Economy_status_Developed                      2
##  9 North America Economy_status_Developing                     1
## 10 Oceania Economy_status_Developed                            2
## 11 Oceania Economy_status_Developing                           9
## 12 Rest of Europe Economy_status_Developed                     4
## 13 Rest of Europe Economy_status_Developing                   11
## 14 South America Economy_status_Developing                    12
datatwa2=datatwa2[!datatwa2["mix"]=="Asia Economy_status_Developed",]
datatwa2=datatwa2[!datatwa2["mix"]=="Middle East Economy_status_Developed",]
datatwa2=datatwa2[!datatwa2["mix"]=="North America Economy_status_Developed",]
datatwa2=datatwa2[!datatwa2["mix"]=="North America Economy_status_Developing",]
datatwa2=datatwa2[!datatwa2["mix"]=="Oceania Economy_status_Developed",]
datatwa2 %>% group_by(mix) %>% summarise(n = n()) 
## # A tibble: 9 × 2
##   mix                                                         n
##   <fct>                                                   <int>
## 1 Africa Economy_status_Developing                           51
## 2 Asia Economy_status_Developing                             26
## 3 Central America and Caribbean Economy_status_Developing    19
## 4 European Union Economy_status_Developed                    27
## 5 Middle East Economy_status_Developing                      13
## 6 Oceania Economy_status_Developing                           9
## 7 Rest of Europe Economy_status_Developed                     4
## 8 Rest of Europe Economy_status_Developing                   11
## 9 South America Economy_status_Developing                    12
datatwa2 %>% group_by(mix) %>%  shapiro_test(Thinness_five_nine_years,Thinness_ten_nineteen_years)
## # A tibble: 18 × 4
##    mix                                                variable statistic       p
##    <fct>                                              <chr>        <dbl>   <dbl>
##  1 Africa Economy_status_Developing                   Thinnes…     0.811 1.33e-6
##  2 Africa Economy_status_Developing                   Thinnes…     0.839 6.51e-6
##  3 Asia Economy_status_Developing                     Thinnes…     0.926 6.08e-2
##  4 Asia Economy_status_Developing                     Thinnes…     0.926 6.23e-2
##  5 Central America and Caribbean Economy_status_Deve… Thinnes…     0.946 3.35e-1
##  6 Central America and Caribbean Economy_status_Deve… Thinnes…     0.940 2.68e-1
##  7 European Union Economy_status_Developed            Thinnes…     0.973 6.92e-1
##  8 European Union Economy_status_Developed            Thinnes…     0.971 6.30e-1
##  9 Middle East Economy_status_Developing              Thinnes…     0.918 2.34e-1
## 10 Middle East Economy_status_Developing              Thinnes…     0.924 2.86e-1
## 11 Oceania Economy_status_Developing                  Thinnes…     0.876 1.43e-1
## 12 Oceania Economy_status_Developing                  Thinnes…     0.896 2.29e-1
## 13 Rest of Europe Economy_status_Developed            Thinnes…     0.935 6.25e-1
## 14 Rest of Europe Economy_status_Developed            Thinnes…     0.849 2.23e-1
## 15 Rest of Europe Economy_status_Developing           Thinnes…     0.920 3.16e-1
## 16 Rest of Europe Economy_status_Developing           Thinnes…     0.884 1.16e-1
## 17 South America Economy_status_Developing            Thinnes…     0.906 1.88e-1
## 18 South America Economy_status_Developing            Thinnes…     0.927 3.47e-1
boxM(Y = cbind(datatwa$Thinness_five_nine_years,datatwa$Thinness_ten_nineteen_years), group = factor(datatwa$Region))
## 
##  Box's M-test for Homogeneity of Covariance Matrices
## 
## data:  cbind(datatwa$Thinness_five_nine_years, datatwa$Thinness_ten_nineteen_years)
## Chi-Sq (approx.) = 453.64, df = 24, p-value < 2.2e-16
m2 <- manova(cbind(Thinness_five_nine_years,Thinness_ten_nineteen_years) ~ Region*Economy_status, data = datatwa)
summary(m2)
##                        Df  Pillai approx F num Df den Df    Pr(>F)    
## Region                  8 0.69743  11.0431     16    330 < 2.2e-16 ***
## Economy_status          1 0.10480   9.6001      2    164 0.0001141 ***
## Region:Economy_status   4 0.02408   0.5026      8    330 0.8541490    
## Residuals             165                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary.aov(m2)
##  Response Thinness_five_nine_years :
##                        Df  Sum Sq Mean Sq F value    Pr(>F)    
## Region                  8 175.961 21.9951 34.3828 < 2.2e-16 ***
## Economy_status          1  12.085 12.0851 18.8915 2.412e-05 ***
## Region:Economy_status   4   1.634  0.4084  0.6384    0.6358    
## Residuals             165 105.552  0.6397                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Thinness_ten_nineteen_years :
##                        Df  Sum Sq Mean Sq F value    Pr(>F)    
## Region                  8 172.664 21.5830 37.5591 < 2.2e-16 ***
## Economy_status          1   8.202  8.2017 14.2727 0.0002205 ***
## Region:Economy_status   4   2.091  0.5228  0.9097 0.4597268    
## Residuals             165  94.816  0.5746                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Fisher Discriminant Analysis (Linear Discriminant Analysis

library(MASS)
library(klaR)
library(ggplot2)
library(GGally)
library(mlbench)
library(ggord)
data_lda=subset(data,select = -c(Country,Region))
str(data_lda)
## 'data.frame':    179 obs. of  17 variables:
##  $ Infant_deaths              : num  11.1 2.7 6.6 57 39.7 21.6 9.6 41.3 2.2 17.4 ...
##  $ Under_five_deaths          : num  13 3.3 8.2 88 59.8 25.2 11.2 59 2.7 21.8 ...
##  $ Adult_mortality            : num  105.8 57.9 223 340.1 261.7 ...
##  $ Alcohol_consumption        : num  1.32 10.35 8.06 4.55 2.69 ...
##  $ Hepatitis_B                : num  97 97 97 84 97 95 99 69 88 97 ...
##  $ Measles                    : num  65 94 97 64 64 99 98 64 91 65 ...
##  $ BMI                        : num  27.8 26 26.2 24.3 23.9 25.5 26.3 21.3 26.6 21.7 ...
##  $ Polio                      : num  97 97 97 77 96 95 99 68 95 97 ...
##  $ Diphtheria                 : num  97 97 97 84 97 95 99 69 95 97 ...
##  $ Incidents_HIV              : num  0.08 0.09 0.08 1.12 0.96 0.05 0.05 0.24 0.04 0.12 ...
##  $ GDP_per_capita             : num  11006 25742 9313 1383 661 ...
##  $ Population_mln             : num  78.53 46.44 144.1 23.3 2.09 ...
##  $ Thinness_ten_nineteen_years: num  4.9 0.6 2.3 5.6 7.3 6 7.1 7.1 0.8 14.2 ...
##  $ Thinness_five_nine_years   : num  4.8 0.5 2.3 5.5 7.2 5.8 6.9 7.1 0.7 14.5 ...
##  $ Schooling                  : num  7.8 9.7 12 6.1 3.4 7.9 9.5 6.1 12.5 8 ...
##  $ Life_expectancy            : num  76.5 82.8 71.2 57.6 60.9 76.1 76.9 65.5 82.3 75.1 ...
##  $ Economy_status             : Factor w/ 2 levels "Economy_status_Developed",..: 2 1 2 2 2 2 2 2 1 2 ...
#make this example reproducible
set.seed(467)

#Use 80% of dataset as training set and remaining 20% as testing set
sample <- sample(c(TRUE, FALSE), nrow(data), replace=TRUE, prob=c(0.8,0.2))
train <- data_lda[sample, ]
test <- data_lda[!sample, ] 
model <- lda(Economy_status~.,data = train)
model
## Call:
## lda(Economy_status ~ ., data = train)
## 
## Prior probabilities of groups:
##  Economy_status_Developed Economy_status_Developing 
##                 0.2255639                 0.7744361 
## 
## Group means:
##                           Infant_deaths Under_five_deaths Adult_mortality
## Economy_status_Developed       3.573333           4.29000        79.24293
## Economy_status_Developing     29.301942          39.26796       189.34433
##                           Alcohol_consumption Hepatitis_B  Measles      BMI
## Economy_status_Developed             9.727333    91.30000 89.93333 26.44333
## Economy_status_Developing            3.353592    86.12621 76.49515 25.20777
##                              Polio Diphtheria Incidents_HIV GDP_per_capita
## Economy_status_Developed  94.86667   95.23333     0.0750000      36783.267
## Economy_status_Developing 86.25243   85.72816     0.8687379       6456.495
##                           Population_mln Thinness_ten_nineteen_years
## Economy_status_Developed        32.17500                    1.233333
## Economy_status_Developing       50.33204                    5.362136
##                           Thinness_five_nine_years Schooling Life_expectancy
## Economy_status_Developed                  1.173333 12.146667        80.21667
## Economy_status_Developing                 5.476699  7.256311        68.95728
## 
## Coefficients of linear discriminants:
##                                       LD1
## Infant_deaths                2.035438e-02
## Under_five_deaths           -5.244384e-02
## Adult_mortality              2.219491e-03
## Alcohol_consumption         -2.546864e-01
## Hepatitis_B                  5.255349e-02
## Measles                      1.317721e-02
## BMI                          4.961314e-02
## Polio                       -2.223254e-03
## Diphtheria                  -4.900140e-02
## Incidents_HIV               -8.602644e-03
## GDP_per_capita              -2.145562e-05
## Population_mln               2.557071e-04
## Thinness_ten_nineteen_years  1.158591e-02
## Thinness_five_nine_years     1.781007e-02
## Schooling                   -1.635261e-01
## Life_expectancy             -1.411105e-01
plot(model)

model.values <- predict(model)
names(model.values)
## [1] "class"     "posterior" "x"
partimat(as.factor(Economy_status)~.,data=train,method="lda") 

train_predict<- predict(model,train)$class
table_train <- table(Predicted =train_predict, Actual = train$Economy_status)
table_train
##                            Actual
## Predicted                   Economy_status_Developed Economy_status_Developing
##   Economy_status_Developed                        28                         2
##   Economy_status_Developing                        2                       101
sum(diag(table_train))/sum(table_train)
## [1] 0.9699248
test_predict<- predict(model,test)$class
table_test<- table(Predicted =test_predict, Actual = test$Economy_status)
table_test
##                            Actual
## Predicted                   Economy_status_Developed Economy_status_Developing
##   Economy_status_Developed                         7                         1
##   Economy_status_Developing                        0                        38
sum(diag(table_test))/sum(table_test)
## [1] 0.9782609

Cluster Analysis

datacl=data[, c("Infant_deaths", "Under_five_deaths", "Adult_mortality", "Thinness_ten_nineteen_years","Thinness_five_nine_years","Life_expectancy","Region")]
X <- scale(datacl[, c("Infant_deaths", "Under_five_deaths", "Adult_mortality", "Thinness_ten_nineteen_years","Thinness_five_nine_years","Life_expectancy")], center = FALSE, scale = TRUE)
dj <- dist(X)
plot(cc <- hclust(dj), main = "Jets clustering")

cc
## 
## Call:
## hclust(d = dj)
## 
## Cluster method   : complete 
## Distance         : euclidean 
## Number of objects: 179

Divisive Hierarchical Clustering

library(cluster)
library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
res.diana <- diana(datacl[, c("Infant_deaths", "Under_five_deaths", "Adult_mortality", "Thinness_ten_nineteen_years","Thinness_five_nine_years","Life_expectancy")], stand = TRUE)

# Plot the dendrogram
fviz_dend(res.diana, cex = 0.5,
          k = 6, # Cut in four groups
          palette = "jco" # Color palette
          )

K-means Clustering

datacl2=data[, c('Hepatitis_B',
                              'Measles',
                              'Polio','Diphtheria',
                              'Incidents_HIV')]
scatterplotMatrix(datacl2)

library("lattice")
datacl_dist <- dist(datacl_1 <- scale(datacl2, center = FALSE))
levelplot(as.matrix(datacl_dist), xlab = "States", ylab = "States")

sapply(datacl2, var)
##   Hepatitis_B       Measles         Polio    Diphtheria Incidents_HIV 
##    200.720168    261.986567    169.632917    215.908669      2.628673
rge <- sapply(datacl2, function(x) diff(range(x)))
datacl_s <- sweep(datacl2, 2, rge, FUN = "/")
sapply(datacl_s, var)
##   Hepatitis_B       Measles         Polio    Diphtheria Incidents_HIV 
##    0.03385397    0.04306157    0.04412927    0.03134108    0.01287277
n <- nrow(datacl_s)
wss <- rep(0, 6)
wss[1] <- (n - 1) * sum(sapply(datacl_s, var))
for (i in 2:6)
  wss[i] <- sum(kmeans(datacl_s,centers = i)$withinss)

plot(1:6, wss, type = "b", xlab = "Number of groups", ylab = "Within groups sum of squares")

kmeans(datacl_s, centers = 2)$centers * rge
##   Hepatitis_B  Measles    Polio Diphtheria Incidents_HIV
## 1    92.98551 67.87514 21.67550   88.63017     3.2454691
## 2    68.16661 66.88274 85.45122   49.59271     0.7814634
kmeans(datacl_s, centers = 2)$cluster
##    1    2    7   28   44   58   75  102  111  113  122  161  167  174  183  203 
##    2    2    2    1    2    2    2    1    2    2    2    2    2    2    1    2 
##  217  220  242  269  272  301  304  331  334  416  427  444  452  474  488  496 
##    1    1    2    2    2    1    2    1    2    2    1    2    1    2    2    2 
##  499  512  547  557  559  580  585  591  599  609  627  629  639  640  651  688 
##    1    2    1    2    2    2    2    2    2    2    2    2    2    2    2    2 
##  697  700  717  728  733  741  764  766  770  787  810  811  833  838  840  850 
##    2    2    2    2    2    2    2    2    2    1    2    1    2    2    1    2 
##  852  853  869  874  901  903  904  907  957 1000 1011 1058 1064 1067 1068 1117 
##    1    2    2    2    2    2    2    2    1    2    1    2    2    1    2    1 
## 1146 1150 1157 1158 1164 1197 1205 1206 1225 1227 1251 1262 1266 1306 1320 1338 
##    2    2    2    1    2    2    2    2    2    2    2    2    2    2    2    1 
## 1358 1481 1492 1503 1531 1536 1559 1566 1588 1604 1614 1620 1624 1629 1707 1710 
##    2    2    2    1    2    2    2    2    2    2    2    1    2    1    1    2 
## 1713 1716 1722 1732 1785 1801 1810 1820 1824 1844 1875 1882 1905 1948 1950 1976 
##    2    2    2    1    2    2    2    1    2    2    1    2    2    2    2    1 
## 1984 1989 2022 2077 2081 2118 2120 2127 2128 2146 2148 2178 2182 2235 2279 2281 
##    2    2    2    1    2    2    2    2    2    2    1    2    2    1    2    2 
## 2291 2322 2324 2325 2339 2357 2368 2379 2396 2405 2410 2443 2449 2469 2496 2519 
##    2    2    1    2    2    2    2    2    2    2    2    2    2    2    1    2 
## 2526 2582 2618 2621 2642 2651 2662 2680 2702 2711 2713 2728 2738 2753 2754 2821 
##    1    1    2    2    1    2    1    1    2    1    2    2    2    1    2    2 
## 2841 2847 2849 
##    2    2    2

Principal Component Analysis

data_numeric<- data[, c('Infant_deaths',
                              'BMI',
                              'GDP_per_capita',
                              'Schooling',
                              'Life_expectancy',
                              'Under_five_deaths',
                              'Alcohol_consumption',
                              'Hepatitis_B',
                              'Measles',
                              'Polio','Diphtheria',
                              'Incidents_HIV',
                              'Population_mln',
                              'Thinness_ten_nineteen_years',
                              'Thinness_five_nine_years')]
data_dis<- data[, c(
                              'Life_expectancy','Under_five_deaths',
                              'Alcohol_consumption','Infant_deaths',
                              'Hepatitis_B','Measles','Alcohol_consumption',
                              'Polio','Diphtheria','Incidents_HIV',
                              'Thinness_ten_nineteen_years',
                              'Thinness_five_nine_years')]
scatterplotMatrix(data_dis, diagonal="histogram")

res <- cor(data_dis, method="pearson")
corrplot::corrplot(res, method= "color", order = "hclust")

data_dis<-scale(data_dis)
data_dis
##      Life_expectancy Under_five_deaths Alcohol_consumption Infant_deaths
## 1        0.643020804      -0.579830261        -0.910686853  -0.579809404
## 2        1.447385265      -0.880912648         1.501608764  -0.970734215
## 7       -0.033666758      -0.728819483         0.889852733  -0.789233410
## 28      -1.770072577       1.748126333        -0.047816992   1.556315454
## 44      -1.348738812       0.872814653        -0.544701804   0.751196499
## 58       0.591950045      -0.201149322        -1.116386479  -0.091153391
## 75       0.694091564      -0.635701220        -1.143100717  -0.649617406
## 102     -0.761425079       0.847983116        -1.033572344   0.825658367
## 111      1.383546816      -0.899536300         0.331525176  -0.994003549
## 113      0.464273147      -0.306683354        -0.467230516  -0.286615796
## 122     -2.050961754       0.792112158         0.737581581   1.007159172
## 161     -0.531606662       0.559316499         0.376939379   0.746542632
## 167      0.387667007      -0.828145632         1.621822832  -0.896272346
## 174     -0.250717485       0.118556717        -1.199200615   0.262540485
## 183     -1.553021850       1.993337761        -0.069188382   2.300934141
## 203      0.272757799      -0.856081111         1.352009036  -0.952118748
## 217     -1.540254160       1.751230275         0.481124904   1.588892522
## 220     -0.033666758      -0.688468236         0.350225142  -0.719425408
## 242      1.038819190      -0.700884004        -0.411130618  -0.738040875
## 269      1.358011436      -0.862288995        -0.531344685  -0.947464881
## 272      1.281405297      -0.812625921         1.055481004  -0.882310746
## 301     -2.344618621       3.011430778        -1.087000819   2.426588544
## 304      0.094010141      -0.278747875        -0.993500988  -0.198192327
## 331     -0.199646726      -0.061471926        -1.220572004   0.057770346
## 334     -1.846678716       1.875387960        -0.427159160   1.695931458
## 416      0.387667007      -0.387385850        -0.598130278  -0.328500597
## 427     -1.514718780       2.347187163        -1.161800683   2.086856268
## 444      1.370779126      -0.893328416         0.641410327  -0.989349682
## 452     -0.084737517      -0.123550769        -1.241943394  -0.016691522
## 474      0.221687039       0.103037006         0.176582600   0.243925018
## 488      0.438737767      -0.480504113        -0.130631127  -0.449501134
## 496      0.911142291      -0.884016590         2.145421881  -0.980041949
## 499     -1.387041882       2.046104777        -0.854586955   1.844855195
## 512      0.081242451      -0.464984403         0.716210191  -0.389000866
## 547     -0.531606662       0.804527927        -1.169814954   0.983889838
## 557      0.451505457      -0.489815940         0.507839141  -0.435539534
## 559     -0.276252865       0.044062106         0.200625414   0.178770883
## 580      0.566414665      -0.651220930         0.248711041  -0.710117674
## 585     -0.863566598       0.453782466        -0.988158141   0.485926091
## 591      0.464273147      -0.710195831        -1.263314784  -0.747348609
## 599      1.332476056      -0.815729863         0.873824191  -0.877656879
## 609      0.119545521      -0.480504113         0.927252665  -0.430885667
## 627      0.834536152      -0.685364294        -0.106588314  -0.700809941
## 629     -2.612740107       1.952986513        -0.443187702   2.282318674
## 639      0.413202387      -0.700884004        -1.263314784  -0.733387008
## 640     -0.365626694       0.366872087        -0.461887668   0.527810893
## 651      0.362131628      -0.831249574         2.530106896  -0.910233947
## 688     -0.480535902       0.326520839        -0.365716415   0.597618895
## 697      0.643020804      -0.741235252         1.156995105  -0.793887277
## 700     -1.208294224       0.671058415        -0.718344345   0.611580495
## 717     -0.723122010       0.636915052        -0.870615497   0.811696767
## 728      0.362131628      -0.523959303         1.060823851  -0.505347536
## 733      1.281405297      -0.859185053         0.953966902  -0.938157147
## 741     -1.450880331       1.114922139        -0.197416720   1.053697840
## 764     -1.821143337       1.623968648        -0.937401090   1.756431726
## 766      0.400434697      -0.728819483         1.645865645  -0.775271810
## 770     -2.370154000       3.368384122        -0.445859126   3.329438702
## 787     -0.199646726       0.307897187        -1.201872038   0.095001281
## 810      0.119545521      -0.502231708        -0.584773160  -0.477424335
## 811      0.809000773      -0.455672576         0.563939039  -0.416924066
## 833      0.336596248      -0.440152866        -1.183172072  -0.398308599
## 838     -1.067849635       0.820047637         0.836424259   0.807042900
## 840     -0.838031218       0.577940151         0.889852733   0.583657294
## 850      0.106777831      -0.167005959        -1.127072174  -0.012037655
## 852     -2.344618621       2.940040109        -0.058502687   2.594127749
## 853      0.591950045      -0.648116988         0.593324700  -0.663579007
## 869     -0.301788244      -0.381177965         0.967324021  -0.323846731
## 874      1.230334538      -0.871600821         1.498937341  -0.956772615
## 901      0.796233083      -0.679156409        -0.926715395  -0.705463808
## 903     -1.016778876       1.260807419        -1.225914852   1.435314917
## 904      0.183383970      -0.384281908         0.331525176  -0.291269663
## 907      0.745162323      -0.747443136        -0.696972956  -0.793887277
## 957     -1.284900363       0.745553026         0.724224462   0.713965564
## 1000    -0.263485175      -0.266332107         0.072397075  -0.235423262
## 1011    -0.620980491       1.375653278        -1.252629089   1.793662660
## 1058    -1.106152705       0.711409663        -0.795815633   0.709311698
## 1064     1.281405297      -0.905744185         1.012738224  -1.003311282
## 1067    -1.029546566       1.201832519        -1.263314784   1.379468516
## 1068     0.323828558      -0.508439593         0.529210531  -0.482078202
## 1117     0.936677671      -0.725715541        -0.956101056  -0.765964076
## 1146     1.192031468      -0.902640243         1.806151068  -0.998657416
## 1150     0.336596248      -0.502231708        -0.389759228  -0.472770468
## 1157     1.217566848      -0.856081111         1.504280188  -0.942811014
## 1158    -1.795607957       1.909531323         0.903209852   2.049625334
## 1164     0.936677671      -0.548790840         1.322623375  -0.491385935
## 1197     1.575062164      -0.899536300         1.020752495  -1.003311282
## 1205     0.502576216      -0.629493335        -0.309616517  -0.631001939
## 1206     0.540879286      -0.253916338        -1.159129259  -0.156307526
## 1225     0.655788494      -0.790898326         1.480237375  -0.859041412
## 1227    -0.608212801       0.550004672        -1.212557733   0.518503159
## 1251     0.528111596      -0.303579412         1.202409308  -0.188884594
## 1262     0.643020804      -0.502231708        -0.152002517  -0.472770468
## 1266    -0.174111346       0.180635559        -1.017543802   0.420771956
## 1306     1.243102227      -0.868496879         1.835536729  -0.956772615
## 1320     0.004636312      -0.492919882         0.542567650  -0.463462734
## 1338    -1.067849635       0.649330820        -0.715672922   0.653465296
## 1358    -1.195526534       0.494133714        -0.560730346   0.453349024
## 1481    -1.527486470       0.919373785        -0.237488076   0.862889302
## 1492     1.332476056      -0.778482557         0.705524496  -0.831118211
## 1503    -0.850798908       0.534484962        -0.822529870   0.541772493
## 1531     0.630253115      -0.859185053         1.004723953  -0.942811014
## 1536     1.217566848      -0.846769284         0.521196260  -0.919541680
## 1559    -0.148575966      -0.011808852        -0.421816313   0.085693547
## 1566     1.281405297      -0.868496879         1.624494256  -0.947464881
## 1588     0.745162323      -0.831249574         1.311937680  -0.900926213
## 1604    -0.097505207      -0.291163644         0.171239753  -0.170269126
## 1614     1.460152955      -0.849873226         1.306594833  -0.924195547
## 1620     0.234454729      -0.104927116        -0.822529870   0.006577812
## 1624     1.064354570      -0.741235252        -0.988158141  -0.784579543
## 1629    -0.965708117       1.583617400        -1.263314784   1.463238118
## 1707    -0.684818940       0.900750133        -1.255300513   1.049043973
## 1710    -1.246597293       1.118026081        -0.328316483   1.086274908
## 1713     0.068474761      -0.613973625        -0.373730686  -0.603078738
## 1716     0.489808526      -0.787794384         0.660110293  -0.845079811
## 1722     0.285525489      -0.291163644         0.128496973  -0.212153928
## 1732    -0.531606662      -0.086303463        -0.838558413   0.029847146
## 1785     0.694091564      -0.787794384         0.045682838  -0.845079811
## 1801     0.489808526      -0.654324872        -1.084329395  -0.686848341
## 1810     1.217566848      -0.843665342         1.298580562  -0.919541680
## 1820    -1.387041882       1.928154976        -1.231257699   1.314314381
## 1824     0.387667007      -0.545686898        -0.184059602  -0.510001402
## 1844     0.004636312       0.199259212        -1.260643360   0.346310088
## 1875    -1.987123305       3.185251537        -1.263314784   2.794244021
## 1882    -0.071969827      -0.384281908        -0.571416041  -0.291269663
## 1905     0.757930013      -0.707091889         0.339539447  -0.742694742
## 1948     1.038819190      -0.738131310         0.844438530  -0.784579543
## 1950     1.166496088      -0.862288995         1.691279848  -0.942811014
## 1976    -1.169991154       1.757438159        -0.413802042   1.900701597
## 1984     1.179263778      -0.856081111         1.253166359  -0.933503281
## 1989    -0.506071282       0.497237656         0.422353582   0.513849292
## 2022     0.374899318      -0.533271130        -0.507301872  -0.500693669
## 2077    -1.016778876       0.599667746        -0.900001158   0.774465833
## 2081     1.434617575      -0.899536300        -0.777115667  -0.994003549
## 2118     0.553646976      -0.502231708        -1.260643360  -0.477424335
## 2120     0.770697703      -0.831249574         1.533665849  -0.900926213
## 2127     1.409082196      -0.874704763         0.644081751  -0.956772615
## 2128     0.911142291      -0.806418037        -0.021102755  -0.886964613
## 2146     0.553646976      -0.496023824         0.254053888  -0.528616870
## 2148    -0.199646726      -0.108031058        -0.883972616   0.001923945
## 2178    -0.365626694       0.003710858        -0.371059262   0.174117016
## 2182     0.528111596      -0.825041689         1.661894188  -0.900926213
## 2235    -2.625507797       2.843817903        -1.022886649   2.994360293
## 2279     1.396314506      -0.862288995         1.322623375  -0.942811014
## 2281    -0.020899068      -0.260124222        -1.215229157  -0.174922993
## 2291     0.196151660      -0.657428815         0.593324700  -0.658925140
## 2322     0.208919350      -0.548790840         1.213095003  -0.537924603
## 2324    -0.033666758      -0.353242486         0.005611482  -0.249384862
## 2325     1.383546816      -0.896432358         1.774093984  -0.989349682
## 2339     0.081242451      -0.570518435        -1.260643360  -0.565847804
## 2357     0.923909981      -0.772274673         1.082195241  -0.826464344
## 2368     0.591950045      -0.626389393         1.004723953  -0.621694205
## 2379    -0.135808276       0.044062106        -1.252629089   0.178770883
## 2396     1.140960709      -0.893328416         1.298580562  -0.984695815
## 2405     0.081242451      -0.378074023        -0.050488416  -0.319192864
## 2410    -0.633748181       0.686578126         0.630724632   0.862889302
## 2443     1.409082196      -0.911952069         0.782995784  -1.012619016
## 2449    -1.476415711       1.372549336        -0.900001158   1.267775713
## 2469     0.783465393      -0.887120532         3.203305673  -0.984695815
## 2496    -0.110272897      -0.064575869        -0.055831263  -0.007383789
## 2519     0.438737767      -0.697780062         1.261180630  -0.738040875
## 2526    -1.144455775       1.186312808        -0.520658990   1.360853049
## 2582    -1.961587925       1.835036712        -0.851915531   1.961201865
## 2618    -1.476415711       2.148534867         0.614696090   1.677315991
## 2621     0.591950045      -0.505335650        -0.277559432  -0.482078202
## 2642    -0.378394384       0.574836209        -1.153786412   0.895466369
## 2651    -0.557142041      -0.225980859        -0.560730346  -0.137692059
## 2662    -1.782840267       2.378226584        -1.097686513   2.012394400
## 2680     0.157848590      -0.406009502        -0.702315803  -0.356423798
## 2702     0.617485425      -0.713299773        -0.536687533  -0.747348609
## 2711    -0.825263528       0.953517149        -1.060286581   0.914081836
## 2713     1.383546816      -0.852977169         1.907665170  -0.947464881
## 2728     0.515343906      -0.731923426        -1.116386479  -0.775271810
## 2738    -0.123040587      -0.598453914        -1.201872038  -0.598424871
## 2753    -1.131688085       0.143388254         0.660110293   0.234617285
## 2754     0.566414665      -0.449464692        -0.862601226  -0.407616333
## 2821     0.145080900      -0.390489792         0.395639345  -0.333154464
## 2841    -0.940172737       1.059051181        -1.177829225   1.444622651
## 2847     0.272757799      -0.381177965        -0.269545161  -0.323846731
## 2849     0.681323874      -0.747443136        -0.854586955  -0.793887277
##       Hepatitis_B     Measles Alcohol_consumption.1       Polio   Diphtheria
## 1     0.698739316 -0.94087799          -0.910686853  0.67085499  0.618204939
## 2     0.698739316  0.85079393           1.501608764  0.67085499  0.618204939
## 7     0.698739316  1.03613930           0.889852733  0.67085499  0.618204939
## 28   -0.218848939 -1.00265978          -0.047816992 -0.86473379 -0.266520088
## 44    0.698739316 -1.00265978          -0.544701804  0.59407555  0.618204939
## 58    0.557571892  1.15970288          -1.116386479  0.51729611  0.482093397
## 75    0.839906740  1.09792109          -1.143100717  0.82441387  0.754316482
## 102  -1.277604618 -1.00265978          -1.033572344 -1.55574875 -1.287356657
## 111   0.063485909  0.66544856           0.331525176  0.51729611  0.482093397
## 113   0.698739316 -0.94087799          -0.467230516  0.67085499  0.618204939
## 122   0.204653332  0.17119423           0.737581581 -0.32727772  0.141814540
## 161   0.557571892 -0.01415114           0.376939379  0.59407555  0.482093397
## 167   0.486988180  0.72723035           1.621822832  0.44051667  0.482093397
## 174   0.275237044 -0.94087799          -1.199200615  0.13339891  0.209870311
## 183  -0.430600075 -1.00265978          -0.069188382 -0.78795436 -0.470687401
## 203   0.839906740  1.15970288           1.352009036  0.82441387  0.754316482
## 217  -1.630523178 -1.00265978           0.481124904 -2.01642538 -1.627635513
## 220  -4.595039080 -1.43513231           0.350225142 -2.86099921 -4.417922136
## 242   0.345820756  0.60366677          -0.411130618  0.28695779  0.277926083
## 269   0.628155604  1.03613930          -0.531344685  0.51729611  0.482093397
## 272   0.345820756  0.41832139           1.055481004  0.28695779  0.277926083
## 301  -2.901029993 -1.00265978          -1.087000819 -2.78421977 -2.852639397
## 304   0.769323028 -0.94087799          -0.993500988 -0.25049828  0.686260710
## 331  -2.195192874 -0.26127830          -1.220572004 -1.24863099 -2.035970141
## 334  -0.007097803 -1.00265978          -0.427159160 -0.40405716 -0.062352774
## 416   0.698739316  0.17119423          -0.598130278  0.74763443  0.618204939
## 427  -2.336360298 -1.00265978          -1.161800683 -3.16811697 -2.308193226
## 444  -1.418772042  0.91257572           0.641410327  0.74763443  0.686260710
## 452  -0.642351211 -3.04145885          -1.241943394 -0.25049828 -0.674854715
## 474  -0.430600075  0.17119423           0.176582600 -0.09693940 -0.198464316
## 488  -0.360016363  0.97435751          -0.130631127 -0.09693940 -0.062352774
## 496   0.698739316  1.15970288           2.145421881  0.67085499  0.618204939
## 499  -0.360016363  0.17119423          -0.854586955 -1.24863099 -0.402631630
## 512   0.769323028  0.17119423           0.716210191  0.67085499  0.686260710
## 547  -0.360016363 -0.26127830          -1.169814954 -0.63439548 -0.674854715
## 557   0.628155604 -0.01415114           0.507839141  0.74763443  0.550149168
## 559   0.557571892  0.91257572           0.200625414  0.28695779  0.482093397
## 580   0.839906740  1.15970288           0.248711041  0.82441387  0.754316482
## 585   0.557571892  0.48010318          -0.988158141  0.51729611  0.482093397
## 591   0.839906740  0.97435751          -1.263314784  0.82441387  0.754316482
## 599  -2.265776586  0.35653960           0.873824191  0.21017835  0.209870311
## 609   0.345820756  0.54188497           0.927252665  0.82441387  0.277926083
## 627   0.839906740  1.09792109          -0.106588314  0.82441387  0.754316482
## 629   0.416404468  0.10941244          -0.443187702 -0.25049828  0.345981854
## 639   0.769323028  0.97435751          -1.263314784  0.67085499  0.686260710
## 640  -0.007097803 -0.69375083          -0.461887668 -0.17371884 -0.062352774
## 651   0.486988180  0.72723035           2.530106896  0.36373723  0.345981854
## 688   0.839906740  1.15970288          -0.365716415  0.82441387  0.754316482
## 697   0.839906740  0.23297602           1.156995105 -0.17371884  0.754316482
## 700   0.063485909 -1.00265978          -0.718344345 -0.02015996  0.005702998
## 717   0.134069620 -0.13771472          -0.870615497  0.05661947  0.073758769
## 728   0.769323028  1.09792109           1.060823851  0.67085499  0.618204939
## 733   0.486988180  0.72723035           0.953966902  0.51729611  0.482093397
## 741   0.486988180 -0.94087799          -0.197416720  0.44051667  0.414037625
## 764   0.063485909 -1.00265978          -0.937401090 -0.02015996 -0.538743173
## 766   0.345820756  0.41832139           1.645865645  0.21017835  0.209870311
## 770  -0.077681515 -1.24978694          -0.445859126 -0.17371884 -0.130408545
## 787  -3.253948553 -2.05295021          -1.201872038 -2.93777865 -3.192918253
## 810   0.275237044  0.48010318          -0.584773160  0.28695779  0.209870311
## 811  -0.995269771  0.72723035           0.563939039 -1.24863099 -1.015133572
## 833   0.839906740  0.97435751          -1.183172072  0.82441387  0.754316482
## 838   0.769323028 -1.00265978           0.836424259  0.59407555  0.686260710
## 840  -0.501183787 -1.00265978           0.889852733 -0.71117492 -0.538743173
## 850   0.628155604  1.09792109          -1.127072174  0.74763443  0.550149168
## 852  -2.689278857 -1.00265978          -0.058502687 -3.55201416 -2.648472083
## 853   0.839906740  0.91257572           0.593324700  0.82441387  0.754316482
## 869   0.839906740  1.09792109           0.967324021  0.82441387  0.754316482
## 874   0.769323028  0.91257572           1.498937341  0.74763443  0.686260710
## 901   0.839906740  1.15970288          -0.926715395  0.82441387  0.754316482
## 903   0.275237044 -1.00265978          -1.225914852  0.28695779  0.209870311
## 904   0.204653332 -0.07593293           0.331525176 -0.02015996  0.550149168
## 907   0.839906740  1.15970288          -0.696972956  0.82441387  0.754316482
## 957  -0.642351211 -1.00265978           0.724224462 -0.25049828 -0.674854715
## 1000  0.628155604 -0.26127830           0.072397075  0.59407555  0.550149168
## 1011 -1.065853483 -1.62047768          -1.252629089 -1.24863099 -1.083189343
## 1058  0.063485909 -1.06444157          -0.795815633 -0.02015996  0.005702998
## 1064  0.063485909  0.72723035           1.012738224  0.67085499  0.618204939
## 1067 -1.559939466 -2.36185916          -1.263314784 -1.63252818 -1.559579742
## 1068  0.486988180  0.91257572           0.529210531  0.44051667  0.414037625
## 1117 -0.430600075 -1.06444157          -0.956101056 -0.55761604 -0.470687401
## 1146  0.063485909  0.97435751           1.806151068  0.51729611  0.482093397
## 1150  0.275237044  0.17119423          -0.389759228  0.21017835  0.209870311
## 1157  0.769323028  0.29475781           1.504280188  0.82441387  0.754316482
## 1158 -3.324532265 -1.00265978           0.903209852 -3.93591136 -4.894312535
## 1164  0.698739316  0.54188497           1.322623375  0.67085499  0.618204939
## 1197 -0.289432651  0.78901214           1.020752495  0.82441387  0.550149168
## 1205  0.345820756  1.03613930          -0.309616517  0.28695779  0.209870311
## 1206  0.839906740  0.91257572          -1.159129259  0.82441387  0.754316482
## 1225  0.628155604  1.03613930           1.480237375  0.59407555  0.550149168
## 1227  0.134069620 -1.62047768          -1.212557733 -0.25049828  0.073758769
## 1251  0.839906740  0.17119423           1.202409308  0.82441387  0.754316482
## 1262  0.275237044  0.35653960          -0.152002517  0.21017835  0.209870311
## 1266  0.628155604  0.85079393          -1.017543802  0.59407555  0.550149168
## 1306  0.416404468  0.48010318           1.835536729  0.36373723  0.345981854
## 1320  0.063485909  0.72723035           0.542567650 -0.02015996 -0.062352774
## 1338 -0.501183787 -1.00265978          -0.715672922 -0.63439548 -0.538743173
## 1358  0.345820756 -1.00265978          -0.560730346  0.28695779  0.277926083
## 1481 -0.007097803 -1.00265978          -0.237488076 -0.02015996 -0.062352774
## 1492  0.557571892  0.66544856           0.705524496  0.67085499  0.618204939
## 1503  0.134069620 -3.22680422          -0.822529870 -0.40405716  0.073758769
## 1531 -0.360016363  0.85079393           1.004723953  0.05661947  0.073758769
## 1536  0.628155604  0.17119423           0.521196260  0.82441387  0.754316482
## 1559  0.839906740  0.17119423          -0.421816313  0.82441387  0.754316482
## 1566  0.557571892  0.35653960           1.624494256  0.51729611  0.482093397
## 1588  0.486988180  0.97435751           1.311937680  0.44051667  0.414037625
## 1604  0.698739316 -0.94087799           0.171239753  0.67085499  0.618204939
## 1614  0.063485909  0.41832139           1.306594833  0.59407555  0.618204939
## 1620 -0.924686059  0.17119423          -0.822529870 -1.47896931 -0.947077800
## 1624  0.839906740  0.66544856          -0.988158141  0.82441387  0.754316482
## 1629 -0.995269771 -1.00265978          -1.263314784 -1.63252818 -1.015133572
## 1707 -1.277604618  0.91257572          -1.255300513 -1.93964594 -1.287356657
## 1710  0.204653332 -2.05295021          -0.328316483  0.13339891  0.141814540
## 1713  0.769323028  1.09792109          -0.373730686  0.74763443  0.686260710
## 1716  0.486988180  0.35653960           0.660110293  0.51729611  0.482093397
## 1722  0.416404468 -0.50840546           0.128496973  0.36373723  0.345981854
## 1732 -0.642351211 -0.94087799          -0.838558413 -1.32541043 -1.083189343
## 1785 -0.360016363  0.48010318           0.045682838 -1.09507211 -0.402631630
## 1801  0.839906740  1.03613930          -1.084329395  0.82441387  0.754316482
## 1810  0.063485909  0.35653960           1.298580562  0.59407555  0.550149168
## 1820 -1.559939466 -1.00265978          -1.231257699 -0.40405716 -1.559579742
## 1824  0.486988180  1.03613930          -0.184059602  0.59407555  0.414037625
## 1844  0.698739316  0.60366677          -1.260643360  0.74763443  0.618204939
## 1875 -3.183364841 -1.00265978          -1.263314784 -3.16811697 -3.124862482
## 1882  0.839906740  1.15970288          -0.571416041  0.82441387  0.754316482
## 1905  0.557571892  0.78901214           0.339539447  0.51729611  0.482093397
## 1948  0.698739316  0.54188497           0.844438530  0.59407555  0.550149168
## 1950  0.063485909  0.78901214           1.691279848  0.28695779  0.482093397
## 1976 -2.477527722 -1.00265978          -0.413802042 -1.78608706 -2.444304769
## 1984  0.063485909 -0.01415114           1.253166359  0.36373723  0.345981854
## 1989  0.769323028  0.41832139           0.422353582  0.82441387  0.686260710
## 2022  0.698739316  0.97435751          -0.507301872  0.74763443  0.618204939
## 2077 -1.418772042 -0.94087799          -0.900001158 -2.86099921 -1.015133572
## 2081  0.628155604  0.60366677          -0.777115667  0.59407555  0.550149168
## 2118  0.769323028 -0.94087799          -1.260643360  0.74763443  0.686260710
## 2120  0.628155604  0.85079393           1.533665849  0.28695779  0.686260710
## 2127  0.416404468  0.17119423           0.644081751  0.36373723  0.345981854
## 2128  0.839906740  1.15970288          -0.021102755  0.82441387  0.754316482
## 2146  0.204653332 -1.06444157           0.254053888 -0.02015996  0.141814540
## 2148 -1.630523178 -0.94087799          -0.883972616 -0.63439548 -1.627635513
## 2178  0.134069620 -1.18800515          -0.371059262  0.28695779  0.073758769
## 2182  0.063485909  1.15970288           1.661894188  0.82441387  0.754316482
## 2235 -2.830446281 -1.00265978          -1.022886649 -2.86099921 -2.784583625
## 2279  0.416404468  0.78901214           1.322623375  0.36373723  0.345981854
## 2281  0.416404468 -1.00265978          -1.215229157  0.36373723  0.345981854
## 2291  0.486988180  0.66544856           0.593324700  0.21017835  0.414037625
## 2322  0.557571892  0.17119423           1.213095003  0.51729611  0.482093397
## 2324  0.134069620 -3.65927675           0.005611482 -0.78795436  0.073758769
## 2325  0.486988180  0.35653960           1.774093984  0.82441387  0.754316482
## 2339  0.698739316  1.03613930          -1.260643360  0.67085499  0.618204939
## 2357  0.345820756  0.35653960           1.082195241  0.36373723  0.482093397
## 2368  0.486988180  0.41832139           1.004723953  0.36373723  0.414037625
## 2379  0.839906740  0.85079393          -1.252629089  0.74763443  0.754316482
## 2396  0.698739316  0.48010318           1.298580562  0.67085499  0.618204939
## 2405  0.628155604  0.91257572          -0.050488416  0.36373723  0.345981854
## 2410  0.134069620 -0.94087799           0.630724632  0.05661947  0.073758769
## 2443  0.063485909  0.85079393           0.782995784  0.28695779  0.277926083
## 2449  0.063485909 -1.00265978          -0.900001158 -0.48083660  0.005702998
## 2469  0.275237044  0.72723035           3.203305673  0.36373723  0.345981854
## 2496 -0.854102347 -1.43513231          -0.055831263 -0.71117492 -1.899858599
## 2519  0.204653332 -0.01415114           1.261180630  0.05661947  0.073758769
## 2526 -1.630523178  0.17119423          -0.520658990 -1.86286650 -1.899858599
## 2582 -0.289432651 -1.00265978          -0.851915531 -0.55761604 -0.334575859
## 2618  0.275237044 -1.86760484           0.614696090  0.21017835  0.209870311
## 2621 -0.642351211 -0.26127830          -0.277559432 -0.32727772 -0.674854715
## 2642 -0.783518635 -1.00265978          -1.153786412 -1.01829267 -0.810966258
## 2651  0.839906740  0.85079393          -0.560730346  0.82441387  0.754316482
## 2662 -1.630523178 -1.00265978          -1.097686513 -1.63252818 -1.627635513
## 2680 -1.983441738 -1.55869589          -0.702315803 -0.78795436 -1.491523971
## 2702  0.839906740  1.15970288          -0.536687533  0.82441387  0.754316482
## 2711 -0.712934923 -1.00265978          -1.060286581 -1.01829267 -0.742910487
## 2713 -0.077681515 -0.07593293           1.907665170  0.67085499  0.686260710
## 2728  0.839906740  1.15970288          -1.116386479  0.82441387  0.754316482
## 2738 -0.642351211  1.15970288          -1.201872038  0.59407555 -0.674854715
## 2753 -0.854102347 -1.31156873           0.660110293 -0.25049828 -0.879022029
## 2754  0.769323028  1.09792109          -0.862601226  0.74763443  0.686260710
## 2821 -0.007097803  0.17119423           0.395639345 -0.09693940 -0.062352774
## 2841 -0.218848939  0.10941244          -1.177829225 -0.32727772 -0.266520088
## 2847  0.769323028  0.17119423          -0.269545161  0.82441387  0.686260710
## 2849  0.769323028  1.15970288          -0.854586955  0.74763443  0.686260710
##      Incidents_HIV Thinness_ten_nineteen_years Thinness_five_nine_years
## 1      -0.32675665                  0.08510204               0.04913431
## 2      -0.32058883                 -0.95960358              -0.97576220
## 7      -0.32675665                 -0.54658042              -0.54673575
## 28      0.31469667                  0.25517040               0.21597793
## 44      0.21601154                  0.66819355               0.62116958
## 58     -0.34526011                  0.35235232               0.28748234
## 75     -0.34526011                  0.61960259               0.54966517
## 102    -0.22807153                  0.61960259               0.59733477
## 111    -0.35142793                 -0.91101262              -0.92809259
## 113    -0.30208537                  2.34458164               2.36111017
## 122     8.44388396                 -0.13355727              -0.11770930
## 161     3.20740444                  0.44953424               0.35898675
## 167    -0.19723242                 -0.57087590              -0.59440536
## 174    -0.27124627                  2.70901383               2.74246701
## 183    -0.16022550                  1.20269410               1.12170043
## 203    -0.24040717                 -0.64376234              -0.61824016
## 217     0.17283680                  0.91114835               0.85951760
## 220    -0.23423935                 -0.54658042              -0.52290095
## 242    -0.25891063                 -0.69235330              -0.68974457
## 269    -0.32675665                 -0.81383070              -0.83275338
## 272    -0.35759575                 -1.00819454              -1.02343180
## 301    -0.11705076                  0.95973931               0.90718721
## 304    -0.27124627                 -0.83812618              -0.80891858
## 331    -0.29591755                  0.18228396               0.12063872
## 334     0.59841641                  0.61960259               0.57349997
## 416    -0.33292447                 -0.59517138              -0.59440536
## 427     0.08031949                  0.66819355               0.64500438
## 444    -0.32675665                 -0.74094426              -0.76124897
## 452    -0.28358191                 -0.76523974              -0.80891858
## 474    -0.14172204                 -0.30362563              -0.33222253
## 488    -0.27741409                 -0.74094426              -0.73741417
## 496    -0.32675665                 -0.66805782              -0.66590976
## 499    -0.17256114                  0.57101163               0.52583037
## 512    -0.12938640                 -0.25503467              -0.28455292
## 547    -0.27124627                 -1.08108097              -1.07110141
## 557    -0.22807153                 -0.44939851              -0.47523134
## 559    -0.01219781                  0.23087492               0.16830833
## 580    -0.31442101                 -0.23073919              -0.40372694
## 585    -0.31442101                  0.93544383               0.85951760
## 591    -0.29591755                 -0.25503467              -0.28455292
## 599    -0.31442101                 -0.95960358              -0.97576220
## 609    -0.12938640                 -0.18214823              -0.18921371
## 627    -0.35759575                 -0.81383070              -0.78508378
## 629     5.79172119                  0.23087492               0.16830833
## 639    -0.29591755                  0.78967095               0.71650879
## 640    -0.33909229                  5.38151658               5.41196490
## 651    -0.32058883                 -0.47369399              -0.47523134
## 688    -0.32675665                 -0.30362563              -0.30838773
## 697    -0.25274281                 -0.30362563              -0.30838773
## 700     1.22136627                  0.44953424               0.38282155
## 717    -0.20340024                  2.00444492               2.00358813
## 728     1.78263792                  0.27946588               0.33515194
## 733    -0.35142793                 -0.86242166              -0.88042299
## 741    -0.20956807                  0.66819355               0.62116958
## 764     1.78263792                 -0.23073919              -0.26071812
## 766    -0.35759575                 -0.64376234              -0.66590976
## 770     0.14816552                  0.69248903               0.64500438
## 787    -0.29591755                  0.42523876               0.35898675
## 810    -0.26507845                 -0.71664878              -0.73741417
## 811    -0.12938640                 -0.64376234              -0.66590976
## 833    -0.29591755                 -0.13355727              -0.14154411
## 838     0.86363268                  0.52242067               0.45432596
## 840     0.29619321                  0.37664780               0.31131714
## 850    -0.34526011                 -0.42510303              -0.40372694
## 852    -0.01836563                  1.27558054               1.21703964
## 853    -0.27741409                  0.76537547               0.74034359
## 869    -0.36993140                 -0.57087590              -0.54673575
## 874    -0.30208537                 -0.93530810              -0.97576220
## 901    -0.27124627                  2.19880876               2.14659694
## 903    -0.36993140                  0.52242067               0.45432596
## 904    -0.12938640                  0.27946588               0.31131714
## 907    -0.29591755                  0.18228396               0.12063872
## 957     0.90680743                  0.25517040               0.23981273
## 1000   -0.28358191                  0.23087492               0.16830833
## 1011   -0.29591755                  3.55935561               3.57668510
## 1058    0.14199770                  0.40094328               0.35898675
## 1064   -0.32675665                 -0.88671714              -0.90425779
## 1067   -0.35759575                  3.07344602               3.02848464
## 1068   -0.12938640                 -0.25503467              -0.28455292
## 1117   -0.35142793                  0.08510204               0.07296912
## 1146   -0.36993140                 -0.76523974              -0.78508378
## 1150   -0.08621166                 -0.66805782              -0.68974457
## 1157   -0.32675665                 -0.86242166              -0.85658818
## 1158    2.21438535                  0.93544383               0.88335240
## 1164   -0.20340024                 -0.18214823              -0.21304851
## 1197   -0.27124627                 -0.59517138              -0.66590976
## 1205   -0.32675665                 -0.59517138              -0.59440536
## 1206   -0.35759575                  0.44953424               0.38282155
## 1225   -0.36376358                 -0.81383070              -0.80891858
## 1227   -0.31442101                  1.20269410               1.12170043
## 1251   -0.12938640                 -0.06067083              -0.07003970
## 1262   -0.25891063                 -0.59517138              -0.64207496
## 1266   -0.30825319                 -0.23073919              -0.21304851
## 1306   -0.32675665                 -0.64376234              -0.59440536
## 1320   -0.15405768                 -0.44939851              -0.42756174
## 1338    0.88213615                  0.71678451               0.59733477
## 1358    2.44876253                  0.88685287               0.83568280
## 1481    2.00467946                  0.25517040               0.21597793
## 1492   -0.32675665                 -0.91101262              -0.90425779
## 1503    0.33320013                  0.78967095               0.71650879
## 1531   -0.35759575                 -0.66805782              -0.66590976
## 1536   -0.33909229                 -0.91101262              -0.92809259
## 1559   -0.28358191                 -0.81383070              -0.83275338
## 1566   -0.33292447                 -1.03249002              -1.04726661
## 1588   -0.36376358                 -0.74094426              -0.76124897
## 1604   -0.30208537                 -0.30362563              -0.28455292
## 1614   -0.34526011                 -1.00819454              -1.02343180
## 1620   -0.35759575                 -0.81383070              -0.80891858
## 1624   -0.33909229                  0.15798848               0.07296912
## 1629   -0.28358191                  0.78967095               0.69267398
## 1707   -0.35759575                  2.19880876               2.09892734
## 1710    2.38708432                  0.42523876               0.35898675
## 1713   -0.28974973                 -0.52228495              -0.49906615
## 1716   -0.36376358                 -0.61946686              -0.61824016
## 1722   -0.28974973                 -0.61946686              -0.64207496
## 1732   -0.27124627                 -1.05678549              -1.04726661
## 1785   -0.32675665                 -0.54658042              -0.54673575
## 1801   -0.31442101                  0.27946588               0.12063872
## 1810   -0.32675665                 -0.91101262              -0.95192740
## 1820   -0.33909229                  1.22698958               1.14553523
## 1824   -0.32058883                 -0.59517138              -0.57057055
## 1844   -0.36993140                  3.24351438               3.26683266
## 1875   -0.29591755                  0.49812519               0.43049116
## 1882   -0.28974973                 -0.37651207              -0.35605733
## 1905   -0.22807153                 -0.74094426              -0.76124897
## 1948   -0.25891063                 -0.91101262              -0.90425779
## 1950   -0.35759575                 -0.83812618              -0.83275338
## 1976    1.78263792                  0.47382972               0.43049116
## 1984   -0.35759575                 -0.83812618              -0.88042299
## 1989   -0.01219781                  0.27946588               0.26364754
## 2022    0.05564821                  0.57101163               0.52583037
## 2077   -0.12321858                 -0.78953522              -0.78508378
## 2081   -0.33292447                 -0.57087590              -0.57057055
## 2118   -0.35142793                  0.95973931               0.95485681
## 2120   -0.32675665                 -0.64376234              -0.61824016
## 2127   -0.33909229                 -0.95960358              -0.95192740
## 2128   -0.27741409                 -0.25503467              -0.30838773
## 2146   -0.29591755                 -0.83812618              -0.83275338
## 2148   -0.27124627                 -0.74094426              -0.76124897
## 2178   -0.31442101                 -0.64376234              -0.64207496
## 2182   -0.32675665                 -0.71664878              -0.71357937
## 2235    0.31469667                  0.88685287               0.85951760
## 2279   -0.35142793                 -0.95960358              -0.95192740
## 2281   -0.29591755                 -0.42510303              -0.42756174
## 2291   -0.28974973                 -0.44939851              -0.42756174
## 2322   -0.16639332                 -0.49798947              -0.49906615
## 2324   -0.08621166                 -0.25503467              -0.26071812
## 2325   -0.31442101                 -0.86242166              -0.88042299
## 2339   -0.32675665                  0.30376136               0.21597793
## 2357   -0.30208537                 -0.91101262              -0.95192740
## 2368   -0.29591755                 -0.86242166              -0.88042299
## 2379   -0.29591755                  2.63612739               2.71863220
## 2396   -0.33909229                 -0.86242166              -0.85658818
## 2405   -0.21573589                  0.49812519               0.47816076
## 2410   -0.28358191                  1.03262574               1.02636122
## 2443   -0.34526011                 -0.86242166              -0.88042299
## 2449    0.06798385                  0.47382972               0.38282155
## 2469   -0.32675665                 -0.64376234              -0.64207496
## 2496   -0.31442101                 -0.86242166               1.21703964
## 2519   -0.35142793                 -0.49798947              -0.45139654
## 2526    0.03714475                 -0.15785275              -0.16537891
## 2582    0.01247347                  0.23087492               0.21597793
## 2618   -0.27741409                  0.83826191               0.69267398
## 2621   -0.27741409                 -0.81383070              -0.83275338
## 2642   -0.31442101                 -0.64376234               1.55072688
## 2651   -0.30208537                 -0.13355727              -0.21304851
## 2662   -0.13555422                  0.76537547               0.69267398
## 2680   -0.27124627                 -1.05678549              -1.07110141
## 2702   -0.36993140                  2.56324095               2.48028418
## 2711   -0.25891063                 -0.76523974              -0.80891858
## 2713   -0.32058883                 -0.93530810              -0.95192740
## 2728   -0.28974973                  0.71678451               0.64500438
## 2738   -0.27124627                 -1.08108097              -1.07110141
## 2753    3.88586468                 -0.03637535               0.16830833
## 2754   -0.35142793                  0.47382972               0.43049116
## 2821   -0.12938640                 -0.71664878              -0.73741417
## 2841   -0.24040717                  0.25517040               0.19214313
## 2847   -0.30825319                 -0.66805782              -0.68974457
## 2849   -0.34526011                  0.40094328               0.35898675
## attr(,"scaled:center")
##             Life_expectancy           Under_five_deaths 
##                  71.4636872                  31.6804469 
##         Alcohol_consumption               Infant_deaths 
##                   4.7289944                  23.5586592 
##                 Hepatitis_B                     Measles 
##                  87.1005587                  80.2290503 
##       Alcohol_consumption.1                       Polio 
##                   4.7289944                  88.2625698 
##                  Diphtheria               Incidents_HIV 
##                  87.9162011                   0.6097765 
## Thinness_ten_nineteen_years    Thinness_five_nine_years 
##                   4.5497207                   4.5938547 
## attr(,"scaled:scale")
##             Life_expectancy           Under_five_deaths 
##                    7.832270                   32.217096 
##         Alcohol_consumption               Infant_deaths 
##                    3.743322                   21.487508 
##                 Hepatitis_B                     Measles 
##                   14.167575                   16.185999 
##       Alcohol_consumption.1                       Polio 
##                    3.743322                   13.024320 
##                  Diphtheria               Incidents_HIV 
##                   14.693831                    1.621318 
## Thinness_ten_nineteen_years    Thinness_five_nine_years 
##                    4.115992                    4.195546
cov(data_dis)
##                             Life_expectancy Under_five_deaths
## Life_expectancy                   1.0000000        -0.9212079
## Under_five_deaths                -0.9212079         1.0000000
## Alcohol_consumption               0.4487724        -0.4391376
## Infant_deaths                    -0.9305646         0.9899859
## Hepatitis_B                       0.4397991        -0.5286901
## Measles                           0.5838125        -0.5845977
## Alcohol_consumption.1             0.4487724        -0.4391376
## Polio                             0.5910969        -0.6650301
## Diphtheria                        0.5370849        -0.5953535
## Incidents_HIV                    -0.4501293         0.3122778
## Thinness_ten_nineteen_years      -0.4563343         0.4789483
## Thinness_five_nine_years         -0.4522485         0.4719123
##                             Alcohol_consumption Infant_deaths Hepatitis_B
## Life_expectancy                      0.44877242    -0.9305646   0.4397991
## Under_five_deaths                   -0.43913759     0.9899859  -0.5286901
## Alcohol_consumption                  1.00000000    -0.4692522   0.2102431
## Infant_deaths                       -0.46925224     1.0000000  -0.5063603
## Hepatitis_B                          0.21024309    -0.5063603   1.0000000
## Measles                              0.31445228    -0.5861101   0.4905367
## Alcohol_consumption.1                1.00000000    -0.4692522   0.2102431
## Polio                                0.28825702    -0.6519378   0.8886645
## Diphtheria                           0.27565589    -0.5814566   0.9438458
## Incidents_HIV                        0.01760975     0.3409592  -0.0767645
## Thinness_ten_nineteen_years         -0.45626812     0.4964201  -0.1234409
## Thinness_five_nine_years            -0.45939934     0.4954018  -0.1398797
##                                Measles Alcohol_consumption.1      Polio
## Life_expectancy              0.5838125            0.44877242  0.5910969
## Under_five_deaths           -0.5845977           -0.43913759 -0.6650301
## Alcohol_consumption          0.3144523            1.00000000  0.2882570
## Infant_deaths               -0.5861101           -0.46925224 -0.6519378
## Hepatitis_B                  0.4905367            0.21024309  0.8886645
## Measles                      1.0000000            0.31445228  0.5571360
## Alcohol_consumption.1        0.3144523            1.00000000  0.2882570
## Polio                        0.5571360            0.28825702  1.0000000
## Diphtheria                   0.5305231            0.27565589  0.9296290
## Incidents_HIV               -0.1843985            0.01760975 -0.1342147
## Thinness_ten_nineteen_years -0.2806768           -0.45626812 -0.2212835
## Thinness_five_nine_years    -0.3048480           -0.45939934 -0.2375340
##                             Diphtheria Incidents_HIV
## Life_expectancy              0.5370849   -0.45012933
## Under_five_deaths           -0.5953535    0.31227776
## Alcohol_consumption          0.2756559    0.01760975
## Infant_deaths               -0.5814566    0.34095920
## Hepatitis_B                  0.9438458   -0.07676450
## Measles                      0.5305231   -0.18439848
## Alcohol_consumption.1        0.2756559    0.01760975
## Polio                        0.9296290   -0.13421473
## Diphtheria                   1.0000000   -0.12232658
## Incidents_HIV               -0.1223266    1.00000000
## Thinness_ten_nineteen_years -0.1821165    0.08962638
## Thinness_five_nine_years    -0.2107806    0.08353299
##                             Thinness_ten_nineteen_years
## Life_expectancy                             -0.45633430
## Under_five_deaths                            0.47894832
## Alcohol_consumption                         -0.45626812
## Infant_deaths                                0.49642015
## Hepatitis_B                                 -0.12344090
## Measles                                     -0.28067679
## Alcohol_consumption.1                       -0.45626812
## Polio                                       -0.22128352
## Diphtheria                                  -0.18211650
## Incidents_HIV                                0.08962638
## Thinness_ten_nineteen_years                  1.00000000
## Thinness_five_nine_years                     0.97313553
##                             Thinness_five_nine_years
## Life_expectancy                          -0.45224853
## Under_five_deaths                         0.47191227
## Alcohol_consumption                      -0.45939934
## Infant_deaths                             0.49540181
## Hepatitis_B                              -0.13987969
## Measles                                  -0.30484804
## Alcohol_consumption.1                    -0.45939934
## Polio                                    -0.23753399
## Diphtheria                               -0.21078062
## Incidents_HIV                             0.08353299
## Thinness_ten_nineteen_years               0.97313553
## Thinness_five_nine_years                  1.00000000
my_data1<-data_dis[,-1]
pca1 <- prcomp(my_data1)
summary(pca1)
## Importance of components:
##                           PC1    PC2    PC3    PC4     PC5     PC6     PC7
## Standard deviation     2.3268 1.4661 1.1195 0.9732 0.76029 0.69642 0.30678
## Proportion of Variance 0.4922 0.1954 0.1139 0.0861 0.05255 0.04409 0.00856
## Cumulative Proportion  0.4922 0.6876 0.8015 0.8876 0.94017 0.98426 0.99281
##                            PC8    PC9    PC10      PC11
## Standard deviation     0.21680 0.1555 0.08864 3.576e-16
## Proportion of Variance 0.00427 0.0022 0.00071 0.000e+00
## Cumulative Proportion  0.99709 0.9993 1.00000 1.000e+00
names(pca1)
## [1] "sdev"     "rotation" "center"   "scale"    "x"
pca1$rotation
##                                    PC1          PC2         PC3         PC4
## Under_five_deaths            0.3770769  0.026875667  0.21508825 -0.12849342
## Alcohol_consumption         -0.2731855  0.354294863  0.40288581  0.34538437
## Infant_deaths                0.3797510  0.001736199  0.22387944 -0.15621322
## Hepatitis_B                 -0.3072257 -0.392227253  0.18505494 -0.17930566
## Measles                     -0.2968243 -0.115896412 -0.06685362  0.07182463
## Alcohol_consumption.1       -0.2731855  0.354294863  0.40288581  0.34538437
## Polio                       -0.3489578 -0.331069284  0.10972589 -0.12290568
## Diphtheria                  -0.3359905 -0.355958968  0.15622617 -0.14393938
## Incidents_HIV                0.1017552  0.077988083  0.63509722 -0.52655172
## Thinness_ten_nineteen_years  0.2591817 -0.416570745  0.23049121  0.42502203
## Thinness_five_nine_years     0.2639296 -0.406231220  0.21758970  0.43528388
##                                    PC5         PC6           PC7         PC8
## Under_five_deaths            0.1966914  0.51284804 -0.1119783725  0.02606432
## Alcohol_consumption          0.1085482  0.07751095  0.0000541613 -0.01575125
## Infant_deaths                0.1766560  0.47720009 -0.0623281063 -0.06381062
## Hepatitis_B                  0.2412358  0.11404922  0.5971791767 -0.47782446
## Measles                     -0.7538204  0.56560550  0.0099238152 -0.00801078
## Alcohol_consumption.1        0.1085482  0.07751095  0.0000541613 -0.01575125
## Polio                        0.1483225 -0.01189170 -0.7885633376 -0.30132749
## Diphtheria                   0.2358806  0.10079643  0.0684134198  0.75848719
## Incidents_HIV               -0.4220445 -0.35112536  0.0074111550  0.02671210
## Thinness_ten_nineteen_years -0.1151151 -0.09933940 -0.0131807329  0.23183170
## Thinness_five_nine_years    -0.1052967 -0.14448392  0.0106491250 -0.21403669
##                                      PC9         PC10          PC11
## Under_five_deaths           -0.091981271  0.686248892 -7.305594e-16
## Alcohol_consumption         -0.001557311 -0.014010727  7.071068e-01
## Infant_deaths                0.120641680 -0.706981820  5.551115e-16
## Hepatitis_B                 -0.168089884  0.031288345 -3.053113e-16
## Measles                      0.022749625  0.000381374  1.387779e-16
## Alcohol_consumption.1       -0.001557311 -0.014010727 -7.071068e-01
## Polio                       -0.080613842 -0.014353299  5.551115e-17
## Diphtheria                   0.263607391 -0.002604673  2.498002e-16
## Incidents_HIV                0.004503998  0.027553446 -1.387779e-16
## Thinness_ten_nineteen_years -0.660425909 -0.111003971 -1.110223e-16
## Thinness_five_nine_years     0.660331970  0.120721093  0.000000e+00
pca1$x
##              PC1          PC2         PC3          PC4          PC5
## 1    -0.31668153 -1.349962667 -0.80314734 -0.598685892  0.831893787
## 2    -2.96912843  0.994966137  0.40866772  0.402701887  0.102292698
## 7    -2.34396852  0.197585647  0.16132159  0.311076427 -0.198373053
## 28    2.18763030  0.429510795  0.88158225 -0.352140966  0.935366119
## 44    0.93902882 -1.449646123  0.70146741 -0.524422777  1.110956686
## 58   -0.22645848 -1.783081029 -0.88100372 -0.424039331 -0.772405840
## 75   -0.71637284 -2.334651074 -0.86977286 -0.203696782 -0.796259310
## 102   3.15860690  0.363916458 -0.87886520  0.225125686 -0.036496686
## 111  -1.97415159  0.493237783 -0.68466065 -0.202829620 -0.225510677
## 113   0.85368988 -2.906389819  0.71808889  1.580445314  0.519730587
## 122   1.02455895  1.265415506  6.30914116 -4.308345791 -3.136848736
## 161   0.28969926 -0.384872050  3.05453273 -1.513051280 -0.772484563
## 167  -2.54483849  0.996547926  0.70701061  0.810587613 -0.009249886
## 174   2.27560836 -3.227605314  0.32812408  1.439817239  0.168153567
## 183   3.11770315 -0.247120966  1.13500155  0.590224213  1.018640276
## 203  -2.92095869  0.428647471  0.54273361  0.499317756 -0.173781339
## 217   3.53052129  1.678191122  0.91663000  1.231960563  0.140729614
## 220   3.29277537  5.138668262 -2.17398076  1.814576707 -1.462743989
## 242  -1.18670857 -0.162559408 -1.02281301 -0.630738442 -0.359404577
## 269  -1.70163633 -0.458830499 -1.22298022 -0.815739506 -0.572143210
## 272  -2.20990149  1.154321889 -0.09308159  0.178408275  0.164387710
## 301   6.24613563  1.728713909 -0.56159670  0.548506159 -0.401445448
## 304  -0.19612237 -0.409280820 -1.16132844 -1.458522481  1.010173129
## 331   2.58637701  1.014944884 -1.94730526  0.262908357 -1.173711760
## 334   2.41917300 -0.418791807  1.09815990 -0.615194314  0.870937445
## 416  -1.02312630 -0.732857493 -0.82030590 -0.942335598  0.303756888
## 427   5.56039602  1.612435701 -0.69226790  0.160862812 -0.422779474
## 444  -1.81567390  0.980103301 -0.57506562  0.367450572 -0.665290155
## 452   1.59922912  0.669485337 -1.61198327 -1.342793821  1.937495816
## 474   0.03619219  0.630496493 -0.14599313  0.001585366 -0.062678436
## 488  -0.81923439  0.562895580 -0.96880353 -0.292680274 -0.772680969
## 496  -3.26057101  1.167462296  1.03473321  1.133502773 -0.056639091
## 499   2.83905654 -0.334220096  0.02297517 -0.290716026 -0.001515220
## 512  -1.62059039 -0.081899690  0.49887201  0.144242260  0.427153636
## 547   1.36194450  0.680458049 -1.42798951 -1.627140236  0.286629108
## 557  -1.52719730  0.020313497  0.13967682 -0.080723698  0.537857609
## 559  -0.62638375 -0.612910953  0.44222338  0.143717958 -0.352481949
## 580  -1.99286733 -0.612179764 -0.15316244 -0.019042751 -0.369153847
## 585   0.67655085 -2.067725291 -0.18373062 -0.077990984 -0.141879296
## 591  -1.12106239 -1.700602864 -1.34805634 -1.031616045 -0.593430235
## 599  -1.21013698  2.070431373 -0.68830430  0.554334839 -0.514551968
## 609  -1.60991038  0.215720045  0.54365693  0.513502161 -0.011050988
## 627  -2.04591506 -0.463231610 -0.68537921 -0.657068175 -0.279287214
## 629   2.34964214 -0.186679225  4.43837181 -3.877684315 -1.735126956
## 639  -0.47913396 -2.439436134 -0.92485492 -0.113899384 -0.870658784
## 640   3.66947505 -4.620353985  2.04378712  4.354674924 -0.500339454
## 651  -2.93095678  1.615394780  1.37538523  1.627742622  0.169690408
## 688  -0.78684710 -1.028338232 -0.14906373 -0.756372520 -0.075653300
## 697  -1.91895198  0.463154512  0.53614263  0.667182529  0.318388516
## 700   1.50282892 -0.641491238  0.74249234 -1.045130030  0.246047385
## 717   2.00685974 -2.344783554  0.43773870  0.969626104 -0.114259098
## 728  -1.63085734 -0.247961881  2.13759275 -0.025456549 -1.178565213
## 733  -2.40108626  0.722599148 -0.06611978  0.183127986 -0.027599906
## 741   1.08104660 -1.030313524  0.73875216 -0.048136748  1.298434048
## 764   2.31047143  0.013266102  1.00183176 -2.284156128  0.368931488
## 766  -2.22174723  1.327696546  0.56735795  0.888485881  0.220912499
## 770   3.64216425 -0.479311808  1.53443331 -0.799551577  1.810586102
## 787   4.69070896  2.434127040 -2.17883115  0.864849382 -0.571739469
## 810  -0.85623683 -0.184574189 -1.09697754 -0.831173736 -0.241505355
## 811  -0.12733375  1.996044146 -0.64078923  0.548159187 -1.054964444
## 833  -0.86124581 -1.744649550 -1.08813695 -0.951599371 -0.490298624
## 838   0.12526309 -0.345216958  2.18058642 -0.070366820  1.204385193
## 840   1.04408075  1.126819965  1.12674480  0.771683072  0.611180695
## 850  -0.66822523 -1.305949448 -1.14105601 -1.134674010 -0.477937672
## 852   6.02885294  2.304587027  0.47902012  1.486122732 -0.287881461
## 853  -1.52506291 -1.216007986  0.65416212  1.095467062 -0.349971359
## 869  -2.25019450  0.107567027  0.42979678  0.200289859  0.032420173
## 874  -3.04035821  0.900180440  0.45698345  0.370611001  0.093300739
## 901  -0.05222125 -3.490550229  0.03707943  1.291864502 -1.195447356
## 903   1.95036071 -1.424789363 -0.22871806 -0.805299770  1.197844352
## 904  -0.51336291 -0.289519297  0.29593479  0.527444507  0.167977720
## 907  -1.29694128 -1.668637217 -0.73357205 -0.252793019 -0.718751450
## 957   1.18738494  1.092764260  1.40591268  0.199388116  0.397185823
## 1000 -0.66156539 -0.751539841  0.14292275  0.158115698  0.563502534
## 1011  5.32878986 -2.401458300  0.70369538  2.287361395  0.177764436
## 1058  1.48710837 -0.742226034  0.01286762 -0.586217761  0.764647443
## 1064 -2.45478012  0.851427148 -0.07873957  0.243665418 -0.087895980
## 1067  5.50077497 -1.417729603  0.13609934  2.105446580  0.478141268
## 1068 -1.53162813 -0.017761057  0.14839424  0.206559554 -0.363787576
## 1117  0.76439014 -0.146404898 -1.42891541 -0.057523286  0.150006545
## 1146 -2.80083072  1.381987189  0.53415495  0.973058091 -0.163698886
## 1150 -0.79915907 -0.010817464 -0.79140195 -0.762722425 -0.062975381
## 1157 -2.85056490  0.845667542  0.55517459  0.402363004  0.582617991
## 1158  6.04272275  4.584466142  1.66685679  1.386795168 -1.985945000
## 1164 -2.05764639  0.289134659  0.88343119  0.740047871  0.227035856
## 1197 -2.25333129  0.747978550  0.02014628  0.505477486 -0.292007278
## 1205 -1.23666034 -0.198924088 -0.94118558 -0.427123199 -0.639066865
## 1206 -0.41067192 -2.175750108 -0.76107486 -0.492611315 -0.455430237
## 1225 -2.78734156  0.906415156  0.43378701  0.561440772 -0.065223393
## 1227  2.14501338 -1.632823007 -0.30388795  0.055463751  1.046811281
## 1251 -1.74052388 -0.003555485  1.10217406  0.562750961  0.610699312
## 1262 -0.97017822  0.072977934 -0.69472388 -0.442512066 -0.091599498
## 1266 -0.20121509 -1.294304165 -0.77166660 -1.024049928 -0.203880251
## 1306 -2.56430328  1.297250347  0.73170180  1.034007848  0.207345474
## 1320 -1.11068982  0.638971264 -0.11587529  0.266831535 -0.449848495
## 1338  2.17119855 -0.246402187  0.38523010 -0.406343445 -0.016176784
## 1358  1.36229689 -1.114572438  1.90334063 -1.279652428 -0.220656026
## 1481  1.45901867 -0.031909076  1.63230874 -1.329370396  0.119945193
## 1492 -2.31330406  0.460944946 -0.17039720 -0.115155318  0.069419605
## 1503  2.31718889 -0.732662273  0.33073487 -0.466181903  2.137534169
## 1531 -1.80272326  1.205731666 -0.21804899  0.674289928 -0.521881056
## 1536 -2.25376284  0.267372182 -0.28220995 -0.310396505  0.452555213
## 1559 -1.05100106 -0.534589757 -0.51983655 -1.210511248  0.596069021
## 1566 -2.77237473  1.352804029  0.44417813  0.455026867  0.440291201
## 1588 -2.53401021  0.898094046  0.24718480  0.567980321 -0.172870971
## 1604 -0.82975262 -0.275440625  0.07587831 -0.275849394  1.265374443
## 1614 -2.51055955  1.220083690  0.13431631  0.320601691  0.256680421
## 1620  1.01910370  1.223701475 -1.76737067 -0.569242632 -0.663141467
## 1624 -1.00853561 -1.791384192 -0.97513154 -0.500028129 -0.380484512
## 1629  3.71582461 -0.074123817 -0.65197710 -0.065055480  0.285697121
## 1707  3.74239277 -1.164210421 -0.55786660  1.608048691 -1.820714392
## 1710  1.91362980 -0.274503010  2.12318875 -1.681022700  0.896482325
## 1713 -1.60662338 -0.805455908 -0.72299626 -0.621465523 -0.442756698
## 1716 -1.93732350  0.350740630 -0.13671278  0.153683615  0.168155161
## 1722 -0.84026303  0.231163337 -0.26808412 -0.436573674  0.813613187
## 1732  1.16212641  1.433408494 -1.70191275 -0.968600169  0.254856493
## 1785 -0.47663697  1.025469157 -1.05607848  0.258136936 -0.742085566
## 1801 -0.94955845 -1.968031171 -0.98279166 -0.506880141 -0.675853595
## 1810 -2.41492547  1.177877713  0.17344372  0.381585610  0.260977489
## 1820  3.92661796 -0.404306737 -0.47605642  0.376933594  0.177084056
## 1824 -1.43993081 -0.346416890 -0.69407792 -0.455381989 -0.451296005
## 1844  1.69820022 -4.406017107  0.59565018  1.782035643 -0.764329394
## 1875  6.59614184  2.315820031 -1.04458743  0.174425857 -0.351023982
## 1882 -1.30774900 -1.142128120 -0.67036895 -0.739487982 -0.419355065
## 1905 -1.89833609  0.167408185 -0.34352917 -0.261043108 -0.204684370
## 1948 -2.30644506  0.574429692  0.01905035 -0.082331605  0.186859617
## 1950 -2.59646884  1.450200128  0.43055609  0.836573846 -0.057078313
## 1976  4.53169828  2.073427746  0.83584311 -0.414881579 -0.943942499
## 1984 -2.10646454  1.275419845  0.11143819  0.463405547  0.440416495
## 1989 -0.58614097 -0.778389476  0.98841758  0.079547010  0.379888288
## 2022 -0.79409511 -1.676369297 -0.11141389  0.002407280 -0.757276204
## 2077  2.64218339  1.992003061 -1.52605557 -0.747584660 -0.011872172
## 2081 -1.38882328 -0.841781227 -1.28234681 -0.803116364 -0.340570648
## 2118  0.33454855 -2.407209328 -0.63039784 -0.119301085  0.648096671
## 2120 -2.63303074  0.872405901  0.56293027  0.750713647  0.002036702
## 2127 -2.00145216  0.764476989 -0.36744844 -0.093769311  0.259535844
## 2128 -1.94849639 -0.833567994 -0.40489627 -0.146166600 -0.512357179
## 2146 -0.78125203  0.829410978 -0.45366467 -0.372168646  1.055493434
## 2148  1.57087685  1.505451171 -1.80649851 -0.563456298 -0.094997705
## 2178  0.08846912  0.205797384 -0.59974557 -0.826784482  1.213193416
## 2182 -2.87343003  1.016043292  0.57450210  0.813597574 -0.223785654
## 2235  6.35821635  1.827533399 -0.15657570  0.233557080 -0.467308829
## 2279 -2.54684256  1.173077623  0.13595965  0.422039593 -0.048764272
## 2281  0.17282370 -0.831395317 -1.21520850 -1.230850894  0.864797615
## 2291 -1.64070237  0.254811956 -0.05809804  0.247758894 -0.153176413
## 2322 -1.91634149  0.659708977  0.63377188  0.430587105  0.436389846
## 2324  0.92049939  0.805601646 -0.10304428 -0.288902441  2.672186299
## 2325 -2.96750527  1.149913166  0.69975509  0.639388195  0.507657416
## 2339 -0.60278148 -1.985657121 -1.12547205 -0.536244499 -0.772837701
## 2357 -2.21541847  1.018297219  0.06728992  0.182891104  0.251965100
## 2368 -2.04706765  0.880565331  0.12412467  0.116093768  0.255718012
## 2379  1.11464260 -4.055773180  0.34981061  1.270783390 -0.846435077
## 2396 -2.70339483  0.803367845  0.30063829  0.342529970  0.316815324
## 2405 -0.70987363 -1.060785354  0.03757806  0.455420082 -0.559176218
## 2410  0.94518080 -0.390883710  1.23575980  1.138443798  1.084539277
## 2443 -2.11280844  0.901106043 -0.37178855  0.222699816 -0.368485327
## 2449  2.16547870 -0.697774054  0.11645129 -0.688994830  0.876161649
## 2469 -3.37180348  2.311981805  1.77053656  2.007886985  0.280362664
## 2496  1.64393418  1.212078022 -0.63113707  0.710592422  0.399869360
## 2519 -1.61964174  1.113406352  0.32126859  0.797751338  0.345179388
## 2526  2.90632839  1.713852227 -0.72287481 -0.076228550 -0.866219667
## 2582  2.71382469 -0.200442790  0.15546541 -0.848487640  0.992239867
## 2618  1.80905687 -0.191788970  1.73233102  0.450851480  2.354917166
## 2621 -0.06506489  1.075380569 -1.22797665 -0.380023873 -0.112091892
## 2642  2.56379348 -0.137541417 -0.93260837 -0.133436188  0.288777640
## 2651 -1.00442428 -1.254498358 -0.49339361 -0.626619478 -0.163726425
## 2662  4.54322815  0.554402210 -0.34949618 -0.024734840  0.217558289
## 2680  1.35920403  2.095398398 -1.96425344 -0.594632580  0.281426806
## 2702 -0.12161926 -3.510233066  0.42856251  1.924316923 -1.160326900
## 2711  1.96940109  0.900506040 -1.25413700 -1.250842678  0.658947236
## 2713 -2.66828247  1.651394156  0.68676729  0.759528403  0.722083124
## 2728 -0.77730852 -2.400569884 -0.82280643 -0.095238178 -0.922809675
## 2738 -0.51418381  0.156633223 -2.12228298 -1.220132236 -1.232874290
## 2753  1.24736421  1.604676707  2.87621995 -1.371142382 -0.902437035
## 2754 -0.70602280 -1.944481489 -0.64508420 -0.150365381 -0.668517881
## 2821 -0.87731600  0.894509699 -0.28072550 -0.147475543  0.005135308
## 2841  1.92237151 -0.730346959 -0.57527156 -0.730994824  0.012980408
## 2847 -1.31143477 -0.506163578 -0.54292139 -0.834241203  0.429620060
## 2849 -1.02492282 -1.894751261 -0.82176779 -0.107113756 -0.826880865
##                PC6           PC7           PC8           PC9          PC10
## 1    -1.014187e+00  0.0191654457 -0.0085256179 -0.0689819974  0.0352715808
## 2     2.818884e-01  0.0981887370 -0.1044396478 -0.0419968989  0.0305279170
## 7     3.556468e-01  0.0706971544 -0.0905103420 -0.0174672252  0.0295722795
## 28    8.560820e-01  0.2315307689  0.1401156617  0.0160529509  0.1129982422
## 44    5.750660e-02 -0.1640578203 -0.0162534639 -0.0432902080  0.1012599961
## 58    4.869355e-01 -0.0065168283 -0.0192507501 -0.0153989104 -0.0470251860
## 75   -4.995075e-02  0.0206514501 -0.0087360812 -0.0479514782  0.0560147122
## 102  -2.231903e-01  0.2157994193  0.1225252774 -0.0129597262  0.0095393683
## 111  -1.102175e-01 -0.1681840027  0.1817154515  0.0388634767  0.0491089981
## 113  -1.232608e+00 -0.0346255010 -0.0044547252 -0.0255524047  0.0319823255
## 122  -1.795041e+00  0.3033867948  0.2599504802  0.1281182287  0.0549449419
## 161  -4.240815e-01 -0.1901074821 -0.0115349613 -0.0227954543 -0.0650544310
## 167   1.210706e-01  0.1321484465 -0.0314745447 -0.0271191609  0.0140020310
## 174  -1.051137e+00  0.0259116833  0.0529255487  0.0220177910 -0.0419685092
## 183   1.229983e+00 -0.0496708258  0.0359734342  0.0291497019 -0.2606791212
## 203   3.718439e-01  0.0700589427 -0.1143870343 -0.0069147667  0.0508859408
## 217   5.623819e-01  0.1984062829  0.1211810180 -0.0195334501  0.0541460142
## 220  -2.177070e+00 -0.6825978962 -0.2858431806 -0.2041546063 -0.0743068471
## 242  -1.105500e-01  0.1295388383 -0.0237587744 -0.0169334142  0.0449821390
## 269   3.930237e-02  0.1654558126 -0.0631005672 -0.0438575585  0.0851574019
## 272   6.111064e-05  0.1492412891 -0.0666192466 -0.0450437813  0.0211857001
## 301   1.196154e+00 -0.2344444266  0.0525786540 -0.0788876172  0.3374951148
## 304  -4.684446e-01  0.7384514576  0.2442054267  0.0733444443 -0.0099046676
## 331  -7.133180e-01 -0.4683398458 -0.0753045551 -0.0986249656 -0.1082081641
## 334   7.809376e-01 -0.0132079203  0.0768806257  0.0001427998  0.1222609472
## 416   4.369162e-02 -0.0654557056 -0.0815690888 -0.0139361184 -0.0221163303
## 427   8.031676e-01  0.5408004317  0.3119211149  0.0413152758  0.1518488500
## 444  -1.178711e-01 -1.2198074014  0.9679241908  0.3258806614 -0.0067824738
## 452  -1.829959e+00 -0.2483056903 -0.0799655592 -0.1357514244 -0.0746122476
## 474   3.534096e-01 -0.2198896291  0.0615475757  0.0316789402 -0.1284963097
## 488   3.012885e-01 -0.0514819517  0.1450591403  0.0655862182 -0.0320521286
## 496   4.788156e-01  0.1016628995 -0.1255779351 -0.0257786478  0.0219285124
## 499   1.755152e+00  0.3963798577  0.2192618471  0.0652893168  0.1269160964
## 512   4.457395e-02  0.0548242541 -0.0621359080 -0.0250388448 -0.0610347957
## 547   8.088393e-01  0.0857972058 -0.1801706572 -0.0183746666 -0.1279804530
## 557  -7.672738e-02 -0.0957160124 -0.1175694718 -0.0482701522 -0.0487325168
## 559   7.209675e-01  0.1313279348  0.0060563676  0.0064872837 -0.0949987203
## 580   3.753186e-01  0.0282079546 -0.0418720030 -0.1245809046  0.0293063918
## 585   5.822890e-01 -0.1239189723 -0.0240332544 -0.0290972204 -0.0042350274
## 591  -3.322494e-02  0.0368557450 -0.0225618784 -0.0283319565  0.0750485474
## 599  -3.930864e-01 -1.3548488698  1.1608370387  0.3817775225 -0.0580505566
## 609   1.467079e-01 -0.3390043717 -0.2266226638 -0.0549017300 -0.0588181459
## 627   4.004102e-01  0.0341040234 -0.0863761502  0.0124558226  0.0267256356
## 629   8.835867e-02  0.1516371489  0.2294977301  0.1257271435 -0.0908673616
## 639  -2.832884e-01  0.1061171176  0.0331005767 -0.0501183528  0.0766238640
## 640  -1.226474e+00  0.0317572953  0.0846236129  0.0324204171 -0.0596497398
## 651   2.572545e-01  0.1837721599 -0.1456537385 -0.0470801340 -0.0020519798
## 688   1.403351e+00 -0.1609687234 -0.1181123105  0.0562024716 -0.1877879821
## 697  -1.104996e-01  0.8239344762  0.2050467219  0.0415137039  0.0365789612
## 700  -5.632373e-01 -0.0618874151  0.0440960433 -0.0546520032  0.0801117449
## 717   1.059900e-01 -0.0895025863 -0.0014227789  0.0295919993 -0.0954695693
## 728  -2.844617e-01  0.0869824167 -0.0837995355  0.0332435045  0.0397854669
## 733   1.051483e-01  0.0772711785 -0.0421976665 -0.0304432478  0.0335110690
## 741   5.213340e-01 -0.2318565165 -0.0594561994 -0.0365060687  0.0282195081
## 764   3.464295e-01 -0.2709472754 -0.4151503851 -0.1201745329 -0.0544980699
## 766   9.183721e-02  0.1881425346 -0.1103832736 -0.0580256201 -0.0095339108
## 770   2.306326e+00 -0.5166386035 -0.0836061939  0.0267289386 -0.0248041187
## 787  -1.792454e+00  0.0901182431  0.0883757265 -0.1628366038  0.1136783759
## 810   1.544492e-02  0.0427651414 -0.0422381087 -0.0275704584 -0.0033844677
## 811   7.071321e-02  0.4055460276  0.0628099179 -0.0083892387 -0.0565406097
## 833   2.515219e-01 -0.0152077907 -0.0427673717  0.0028947795  0.0151342836
## 838   9.730063e-02 -0.1097289225 -0.0275932947 -0.0409084212  0.0027803420
## 840  -1.436496e-01  0.1142497055  0.0315617675 -0.0506114257 -0.0414776300
## 850   6.948705e-01 -0.1478281930 -0.1063868125  0.0341641745 -0.0776696997
## 852   1.341996e+00  0.5089624620  0.3022011543  0.0212696726  0.1634153071
## 853   3.551755e-02  0.0218726910 -0.0665908539 -0.0281742055  0.0173440828
## 869   8.485373e-01 -0.0240928863 -0.1313530259  0.0234886427 -0.0596607571
## 874   3.329426e-01  0.0829671355 -0.1046148239 -0.0558311423  0.0258880548
## 901  -4.439945e-01  0.0263742019  0.0126684064 -0.0380704719  0.0791606882
## 903   6.358664e-01 -0.2930765775 -0.0568845165 -0.0225580715 -0.1249349800
## 904  -2.759046e-01  0.2348904072  0.3190015235  0.1301192586 -0.0588541036
## 907   1.610569e-02  0.0443787419 -0.0252305405 -0.0493233658  0.0669616555
## 957  -2.484838e-01 -0.3641808685 -0.1383139681 -0.0633199199 -0.0029356023
## 1000 -2.131401e-01 -0.0171477116 -0.0440603162 -0.0611413550 -0.0218877433
## 1011 -5.316456e-01 -0.0190610332  0.0895204559  0.0609477934 -0.2736441574
## 1058 -1.555954e-01 -0.0807315090  0.0068513323 -0.0362469519  0.0136319584
## 1064  2.007768e-02 -0.2778844337  0.2183500625  0.0609010521  0.0306658699
## 1067 -1.190099e+00 -0.0059518422  0.1111629375 -0.0428124505 -0.1227330579
## 1068  3.113119e-01  0.0672368542 -0.0595412633 -0.0205561322 -0.0243477646
## 1117 -1.473494e+00  0.2657583407  0.0800977689 -0.0632408839  0.0553226298
## 1146  2.606432e-01 -0.1648566775  0.1356938959  0.0390999613  0.0096387471
## 1150 -2.004295e-01  0.1011688791 -0.0172283538 -0.0282618284 -0.0058656785
## 1157 -1.089838e-02  0.0184645684 -0.0811058926 -0.0274483632  0.0306195603
## 1158 -2.934802e-01  0.4455976971 -0.9522241642 -0.3925738659 -0.1352882152
## 1164  2.499145e-01  0.0267797683 -0.0981371116 -0.0304662014 -0.0665428099
## 1197 -7.237859e-02 -0.6153612405  0.3065637796  0.0558081286  0.0195963633
## 1205  2.310210e-01  0.1137514717 -0.0866986176 -0.0205357622  0.0146494317
## 1206  3.192693e-01 -0.0543148740 -0.0323199217 -0.0256316047 -0.0319716659
## 1225  4.454469e-01  0.0962582672 -0.1078584041 -0.0186992013  0.0158463243
## 1227 -7.204629e-01  0.1662873351  0.1301334437 -0.0590362418  0.0450712873
## 1251  2.609992e-01 -0.0502311461 -0.1152477328 -0.0102733923 -0.1012251508
## 1262 -1.222868e-02  0.1013010108 -0.0241218546 -0.0422219766 -0.0195516904
## 1266  8.988714e-01 -0.0953394418 -0.0749067967  0.0585331490 -0.1435855176
## 1306 -3.277105e-03  0.1470917306 -0.1001522855 -0.0072675435  0.0267707618
## 1320  1.831855e-01  0.1411313956 -0.0945319624 -0.0074341621 -0.0290695654
## 1338 -6.043827e-01  0.0440902288  0.0896983027 -0.0830745837  0.0149648568
## 1358 -1.188904e+00 -0.0789951127  0.0608861763 -0.0426636236  0.1098089473
## 1481 -4.879581e-01 -0.1455215568  0.0130659654 -0.0330285525  0.0803582503
## 1492  1.437088e-01 -0.0081357478 -0.0208666113  0.0025148778  0.0230026903
## 1503 -1.691399e+00  0.2776957681  0.1833700366 -0.0720535343  0.0234084505
## 1531  2.674455e-04 -0.0920065647  0.1883091671  0.0567772669  0.0207517115
## 1536 -2.139169e-01 -0.0698758629  0.0207747980 -0.0166993784  0.0400640264
## 1559  5.290316e-01 -0.0995308156 -0.0894732838 -0.0058588398 -0.0623270293
## 1566  3.276644e-02  0.1180411439 -0.0969491395 -0.0508668432  0.0162257143
## 1588  3.016097e-01  0.1297797351 -0.0832604159 -0.0373525677  0.0182653086
## 1604 -4.248239e-01 -0.0368145640 -0.0792571887 -0.0130034884 -0.0829389538
## 1614 -5.985071e-03 -0.2313652498  0.2279620517  0.0650023667  0.0044116277
## 1620  5.859332e-02  0.5616766813  0.1654454685  0.0436098933 -0.0759478105
## 1624 -2.765013e-01  0.0376596471 -0.0091129525 -0.0747355024  0.0683649021
## 1629  4.720902e-01  0.3397961771  0.2204975101 -0.0221102177  0.0703764701
## 1707  6.355769e-01  0.5118927596  0.2582217570  0.0323627569 -0.0973182283
## 1710 -1.016536e+00 -0.1706766399  0.0417041436 -0.0582761337  0.0737101633
## 1713  3.341410e-01  0.0334337421 -0.0689095005  0.0152534054  0.0172148074
## 1716 -1.267264e-01  0.0592634098 -0.0341711360 -0.0206801671  0.0291339310
## 1722 -1.841153e-01  0.0254839260 -0.0541003001 -0.0350672074 -0.0634420283
## 1732 -5.073230e-01  0.5866089741 -0.1135601385 -0.0728080595 -0.0720345396
## 1785 -3.492572e-01  0.7656120271  0.2062941314  0.0224238357  0.0469051316
## 1801 -1.815373e-02  0.0245937335  0.0055944191 -0.1108444977  0.0546991327
## 1810 -7.010910e-02 -0.2380027101  0.1846743974  0.0287907818  0.0041142003
## 1820  3.594187e-01 -1.0340355929 -0.2723712630 -0.2095318301  0.3819172993
## 1824  3.786243e-01 -0.0467734127 -0.1062654811  0.0070621778 -0.0143776991
## 1844 -1.177495e-01 -0.1787390742 -0.0294384084  0.0397805760 -0.0388773348
## 1875  1.555873e+00 -0.1616615043  0.0735464827 -0.0540484433  0.1879450412
## 1882  5.838852e-01 -0.0252664088 -0.0791441226  0.0318116863 -0.0380279017
## 1905  1.515683e-01  0.0913370609 -0.0596217792 -0.0303740570  0.0234468653
## 1948  1.245884e-01  0.1239285296 -0.1202954564 -0.0339996242  0.0214175881
## 1950  1.978830e-01  0.0074731093  0.2013279565  0.0735493931  0.0069774895
## 1976 -6.584067e-02 -0.5520153311 -0.1210381721 -0.0584083270 -0.1235332219
## 1984 -3.244275e-01 -0.0721850209  0.1049598868 -0.0163530798  0.0101252771
## 1989  8.878330e-01 -0.2282057862 -0.1239521462 -0.0009414665 -0.0228085354
## 2022 -5.908365e-02 -0.0309688029 -0.0427127903 -0.0320021869  0.0137602426
## 2077  1.044750e-02  1.2156468152  0.7538621326  0.2236524740 -0.1223633084
## 2081 -3.386206e-01  0.1118634344 -0.0213680928 -0.0307223106  0.1024532031
## 2118 -1.174872e+00 -0.0117477402  0.0009970070 -0.0424583187  0.0384463778
## 2120  2.681489e-01  0.3531106447  0.0889496700  0.0499744958  0.0254132283
## 2127 -2.785200e-01  0.1448565633 -0.0573343724 -0.0375622243  0.0473383893
## 2128  1.451521e-01  0.0581897572 -0.0511826077 -0.0516328497  0.0706167111
## 2146 -7.239537e-01  0.2257558940  0.0132084053 -0.0362531250  0.0164759392
## 2148 -7.873274e-01 -0.5826119086 -0.2479147639 -0.1268836234 -0.1058810852
## 2178 -3.580384e-01 -0.1649548762 -0.1046083531 -0.0316731284 -0.1254377363
## 2182  4.230152e-01 -0.4009308522  0.2455881974  0.1107410995 -0.0027798329
## 2235  1.269428e+00 -0.1400512967  0.0558274159  0.0356948739 -0.1633646015
## 2279  1.934713e-01  0.1487092564 -0.0845561293 -0.0251337256  0.0268701064
## 2281 -6.864262e-01  0.0143140136 -0.0103956804 -0.0272303068 -0.0268470210
## 2291  1.196915e-01  0.2739842740 -0.0015068662  0.0177670334 -0.0002561739
## 2322  3.277504e-02  0.0548581494 -0.0892768229 -0.0240550349 -0.0310203996
## 2324 -2.243632e+00  0.7251936138  0.2595341405 -0.0245488338 -0.0578817969
## 2325 -1.011721e-02 -0.1422408499  0.0521548440  0.0029881468  0.0169222765
## 2339  1.538454e-02  0.0357288169  0.0009947462 -0.0563238780  0.0382209786
## 2357 -3.207787e-03  0.0939460643  0.0709528615 -0.0125909181  0.0063623614
## 2368  1.841762e-01  0.1452648758 -0.0593131970 -0.0261741338 -0.0280959685
## 2379  7.102129e-03 -0.0521340605 -0.0107387501  0.0910650462 -0.0197196148
## 2396  7.344252e-03  0.0965996137 -0.0979789701 -0.0359103366  0.0405153851
## 2405  2.214869e-01  0.1801704543 -0.1351611097 -0.0407213320 -0.0220086379
## 2410  2.002430e-01 -0.1042538863 -0.0625348633  0.0044113708 -0.1522619636
## 2443  1.763155e-02  0.0038362532  0.0826481066  0.0047333311  0.0455380966
## 2449  4.895431e-01  0.1730462668  0.1398680652 -0.0235490263  0.0748169847
## 2469  3.164449e-01  0.0687082962 -0.0662674207 -0.0153101983 -0.0146727524
## 2496 -1.117236e+00 -0.0637806783 -1.2753941465  1.0444535264  0.1843462066
## 2519 -2.543550e-01  0.2058983044 -0.0978352758 -0.0193961904  0.0040863183
## 2526  9.451392e-01  0.1498744029 -0.1416733630 -0.0207838269 -0.1540861599
## 2582  1.059183e+00 -0.0944326640  0.0177346651  0.0432600759 -0.1031446610
## 2618  9.053508e-01 -0.3563442064 -0.0524298208 -0.1450216656  0.2586353884
## 2621 -5.188351e-01 -0.0878751014 -0.0957347116 -0.0739659097 -0.0297665213
## 2642 -2.325477e-01  0.1720180631 -0.4212177150  1.4836889290  0.0355660502
## 2651  5.248266e-01 -0.0574001266 -0.0572940427 -0.0373579382 -0.0484324511
## 2662  9.835864e-01 -0.2032389669  0.0382351542 -0.0674324003  0.2112863975
## 2680 -1.380989e+00 -0.6125105600  0.0776528608 -0.0457624936 -0.0738878113
## 2702 -4.707935e-01  0.0308689922  0.0125938634 -0.0619783536  0.0715230402
## 2711  3.334529e-01  0.1521552981  0.0807830092 -0.0207849371  0.0118408084
## 2713 -2.414427e-01 -0.3746152842  0.3125788947  0.0840354207 -0.0027738249
## 2728 -1.630951e-01  0.0400198083 -0.0009558874 -0.0539135973  0.0803440763
## 2738  8.617866e-02 -0.7817101130 -0.3614088145 -0.0993672210  0.0028663556
## 2753 -2.022166e+00 -0.3852086379 -0.1453136221  0.0679293087  0.0241191583
## 2754  2.243954e-01 -0.0009111139 -0.0313695950 -0.0190961008  0.0055644203
## 2821  1.614303e-02  0.1348057254 -0.0292102467 -0.0232686399 -0.0551640339
## 2841  1.095172e+00 -0.1016184582 -0.0157045469  0.0332134708 -0.2747119899
## 2847  1.263836e-01 -0.0800154674 -0.0931307258 -0.0297913012 -0.0321636531
## 2849 -6.115820e-02  0.0573904909 -0.0166634637 -0.0359602634  0.0735911069
##               PC11
## 1     2.275660e-16
## 2     1.206511e-16
## 7     7.565225e-17
## 28   -6.514876e-16
## 44   -3.608457e-16
## 58    3.799828e-16
## 75    5.463842e-16
## 102  -1.120148e-16
## 111   4.100782e-16
## 113  -1.932439e-16
## 122  -1.361783e-15
## 161  -6.191760e-16
## 167  -2.084572e-16
## 174  -9.226490e-17
## 183  -4.391416e-16
## 203   1.169831e-16
## 217  -8.101949e-16
## 220   7.977565e-17
## 242   4.201977e-16
## 269   5.068873e-16
## 272   2.486920e-17
## 301  -8.464312e-16
## 304   2.882163e-16
## 331   3.311090e-16
## 334  -7.449536e-16
## 416   3.082096e-16
## 427  -5.047170e-16
## 444   8.956495e-16
## 452   5.285160e-17
## 474   1.927085e-16
## 488   4.745036e-16
## 496   8.913895e-17
## 499  -3.203601e-16
## 512  -7.812842e-17
## 547   2.869391e-16
## 557   9.394049e-17
## 559   1.401725e-16
## 580   2.479333e-16
## 585   8.892227e-17
## 591   6.366408e-16
## 599   8.803988e-16
## 609   4.234633e-17
## 627   4.019279e-16
## 629  -9.234076e-16
## 639   4.951306e-16
## 640  -5.756289e-16
## 651  -4.624348e-16
## 688   4.242707e-16
## 697  -1.965198e-16
## 700  -3.301237e-16
## 717   4.930193e-17
## 728  -4.198169e-16
## 733   1.826389e-16
## 741  -3.613099e-16
## 764  -4.684931e-16
## 766  -3.685336e-17
## 770  -8.613082e-16
## 787  -3.006814e-16
## 810   3.512395e-16
## 811   1.551125e-16
## 833   5.121318e-16
## 838  -5.285591e-16
## 840  -5.900446e-16
## 850   6.071067e-16
## 852  -1.018651e-15
## 853  -3.432686e-17
## 869   1.268662e-16
## 874   3.586929e-16
## 901   1.387410e-16
## 903   6.169295e-17
## 904   1.232373e-16
## 907   4.215552e-16
## 957  -4.476810e-16
## 1000  3.716568e-18
## 1011 -2.499057e-16
## 1058 -6.391428e-17
## 1064  3.354596e-16
## 1067 -4.387346e-16
## 1068  1.186396e-16
## 1117  1.128351e-16
## 1146  2.854397e-16
## 1150  2.612488e-16
## 1157  1.532426e-16
## 1158 -1.519183e-15
## 1164  1.807300e-17
## 1197  3.979341e-16
## 1205  4.018235e-16
## 1206  4.559552e-16
## 1225  3.112409e-16
## 1227 -8.537168e-17
## 1251 -1.852049e-16
## 1262  2.632458e-16
## 1266  4.608457e-16
## 1306 -2.206528e-16
## 1320  1.100894e-16
## 1338 -2.607719e-16
## 1358 -6.304949e-16
## 1481 -6.007854e-16
## 1492  2.826458e-16
## 1503 -5.820058e-16
## 1531  2.563860e-16
## 1536  2.158603e-16
## 1559  1.973674e-16
## 1566  8.793009e-17
## 1588 -7.244297e-17
## 1604  3.621653e-18
## 1614  3.472521e-16
## 1620  3.764118e-16
## 1624  4.857554e-16
## 1629 -1.704757e-16
## 1707  4.238948e-17
## 1710 -7.797443e-16
## 1713  4.221485e-16
## 1716  1.018662e-16
## 1722  9.070320e-17
## 1732  1.438807e-16
## 1785  2.222188e-16
## 1801  4.688449e-16
## 1810  2.058722e-16
## 1820 -6.122000e-16
## 1824  4.135059e-16
## 1844  1.092102e-16
## 1875 -5.266040e-16
## 1882  4.272269e-16
## 1905  2.352998e-16
## 1948  8.543436e-17
## 1950  2.790335e-16
## 1976 -5.656427e-16
## 1984  1.382726e-16
## 1989 -2.007200e-16
## 2022  2.358343e-16
## 2077  1.364473e-16
## 2081  5.020323e-16
## 2118  1.551481e-16
## 2120  8.213137e-17
## 2127  9.368026e-17
## 2128  3.062102e-16
## 2146 -2.586533e-17
## 2148  3.442385e-16
## 2178  9.394982e-17
## 2182  5.811478e-16
## 2235 -4.414287e-16
## 2279  3.988102e-17
## 2281  3.059028e-16
## 2291  9.417572e-17
## 2322 -1.055445e-16
## 2324 -4.143806e-16
## 2325  1.515307e-16
## 2339  4.253346e-16
## 2357  6.163937e-17
## 2368  1.494107e-16
## 2379  3.113952e-16
## 2396  1.124296e-16
## 2405  1.159486e-16
## 2410 -3.867885e-16
## 2443  3.400401e-16
## 2449 -4.203744e-16
## 2469 -6.647420e-16
## 2496 -2.567192e-16
## 2519 -9.641828e-17
## 2526 -6.602422e-17
## 2582 -1.418943e-16
## 2618 -1.156208e-15
## 2621  2.751728e-16
## 2642  1.890674e-16
## 2651  3.464543e-16
## 2662 -6.743913e-16
## 2680  3.492692e-16
## 2702  1.119762e-16
## 2711  1.008286e-16
## 2713  1.349541e-16
## 2728  4.168689e-16
## 2738  6.881999e-16
## 2753 -8.242300e-16
## 2754  3.201172e-16
## 2821  1.320742e-16
## 2841  2.533562e-16
## 2847  3.063847e-16
## 2849  4.383755e-16
library(factoextra)
fviz_eig(pca1,addlabels=TRUE) #represent the proportion values

pca<-pca1$x[,1:6]
head(pca)
##           PC1        PC2        PC3        PC4        PC5        PC6
## 1  -0.3166815 -1.3499627 -0.8031473 -0.5986859  0.8318938 -1.0141867
## 2  -2.9691284  0.9949661  0.4086677  0.4027019  0.1022927  0.2818884
## 7  -2.3439685  0.1975856  0.1613216  0.3110764 -0.1983731  0.3556468
## 28  2.1876303  0.4295108  0.8815823 -0.3521410  0.9353661  0.8560820
## 44  0.9390288 -1.4496461  0.7014674 -0.5244228  1.1109567  0.0575066
## 58 -0.2264585 -1.7830810 -0.8810037 -0.4240393 -0.7724058  0.4869355
res1 <- cor(pca, method="pearson")
corrplot::corrplot(res1, method= "color", order = "hclust")

biplot(pca1, col = c("gray", "black"))

fviz_pca_var(pca1, col.var = "contrib")

fviz_pca_var(pca1, select.var = list(contrib = 6))

fviz_pca_ind(pca1, col.ind = "#00AFBB")

fviz_contrib(pca1, choice = "ind", axes = 1:2) + coord_flip()

fviz_pca_ind(pca1, label="none", habillage= data$Economy_status,
addEllipses=TRUE, ellipse.level=0.95)

ols.data <- data.frame(Life_expectancy=data_dis[,1],pca)
lmodel <- lm(Life_expectancy ~ ., data = ols.data)
summary(lmodel)
## 
## Call:
## lm(formula = Life_expectancy ~ ., data = ols.data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.81568 -0.23490 -0.01441  0.24825  0.76545 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.654e-16  2.490e-02   0.000    1.000    
## PC1         -3.555e-01  1.073e-02 -33.122  < 2e-16 ***
## PC2          1.532e-03  1.703e-02   0.090    0.928    
## PC3         -2.739e-01  2.231e-02 -12.277  < 2e-16 ***
## PC4          2.461e-01  2.566e-02   9.590  < 2e-16 ***
## PC5         -1.344e-01  3.285e-02  -4.091 6.60e-05 ***
## PC6         -3.108e-01  3.586e-02  -8.668 3.17e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3332 on 172 degrees of freedom
## Multiple R-squared:  0.8927, Adjusted R-squared:  0.889 
## F-statistic: 238.6 on 6 and 172 DF,  p-value: < 2.2e-16
mean((ols.data$Life_expectancy - predict(lmodel))^2) #mse
## [1] 0.1066567
sqrt(mean((ols.data$Life_expectancy - predict(lmodel))^2)) 
## [1] 0.3265834

Factor Analysis

data2
##      Infant_deaths Under_five_deaths Adult_mortality Alcohol_consumption
## 1             11.1              13.0        105.8240                1.32
## 2              2.7               3.3         57.9025               10.35
## 7              6.6               8.2        223.0000                8.06
## 28            57.0              88.0        340.1265                4.55
## 44            39.7              59.8        261.7065                2.69
## 58            21.6              25.2         95.8155                0.55
## 75             9.6              11.2         89.1875                0.45
## 102           41.3              59.0        218.4575                0.86
## 111            2.2               2.7         53.8970                5.97
## 113           17.4              21.8        124.5470                2.98
## 122           45.2              57.2        434.8210                7.49
## 161           39.6              49.7        248.5950                6.14
## 167            4.3               5.0        160.2370               10.80
## 174           29.2              35.5        154.6040                0.24
## 183           73.0              95.9        260.0235                4.47
## 203            3.1               4.1        163.8720                9.79
## 217           57.7              88.1        242.9655                6.53
## 220            8.1               9.5        202.8000                6.04
## 242            7.7               9.1         85.6715                3.19
## 269            3.2               3.9         56.3370                2.74
## 272            4.6               5.5         67.0000                8.68
## 301           75.7             128.7        363.1670                0.66
## 304           19.3              22.7        148.0870                1.01
## 331           24.8              29.7        162.9175                0.16
## 334           60.0              92.1        270.2885                3.13
## 416           16.5              19.2        146.5195                2.49
## 427           68.4             107.3        262.8710                0.38
## 444            2.3               2.9         53.4415                7.13
## 452           23.2              27.7        175.5640                0.08
## 474           28.8              35.0        161.6170                5.39
## 488           13.9              16.2        110.8405                4.24
## 496            2.5               3.2         82.5385               12.76
## 499           63.2              97.6        242.9535                1.53
## 512           15.2              16.7        154.8235                7.41
## 547           44.7              57.6        198.4490                0.35
## 557           14.2              15.9        144.3625                6.63
## 559           27.4              33.1        209.3720                5.48
## 580            8.3              10.7         82.2730                5.66
## 585           34.0              46.3        255.7810                1.03
## 591            7.5               8.8         58.1365                0.00
## 599            4.7               5.4         65.9695                8.00
## 609           14.3              16.2        141.3000                8.20
## 627            8.5               9.6         75.2050                4.33
## 629           72.6              94.6        513.4755                3.07
## 639            7.8               9.1         87.9740                0.00
## 640           34.9              43.5        177.9465                3.00
## 651            4.0               4.9        165.2330               14.20
## 688           36.4              42.2        189.9280                3.36
## 697            6.5               7.8        130.0025                9.06
## 700           36.7              53.3        294.8580                2.04
## 717           41.0              52.2        196.0530                1.47
## 728           12.7              14.8        151.6085                8.70
## 733            3.4               4.0         58.0775                8.30
## 741           46.2              67.6        294.1870                3.99
## 764           61.3              84.0        332.5830                1.22
## 766            6.9               8.2        136.0675               10.89
## 770           95.1             140.2        397.8705                3.06
## 787           25.6              41.6        178.1065                0.23
## 810           13.3              15.5        182.1595                2.54
## 811           14.6              17.0        114.7010                6.84
## 833           15.0              17.5        109.9420                0.30
## 838           40.9              58.1        239.6670                7.86
## 840           36.1              50.3        238.5125                8.06
## 850           23.3              26.3        124.8970                0.51
## 852           79.3             126.4        356.2145                4.51
## 853            9.3              10.8        148.8890                6.95
## 869           16.6              19.4        212.8410                8.35
## 874            3.0               3.6         73.2830               10.34
## 901            8.4               9.8         68.3620                1.26
## 903           54.4              72.3        227.2735                0.14
## 904           17.3              19.3        168.7145                5.97
## 907            6.5               7.6         68.5765                2.12
## 957           38.9              55.7        311.7215                7.44
## 1000          18.5              23.1        191.5860                5.00
## 1011          62.1              76.0        160.1410                0.04
## 1058          38.8              54.6        244.6325                1.75
## 1064           2.0               2.5         68.8685                8.52
## 1067          53.2              70.4        227.7350                0.00
## 1068          13.2              15.3        174.4925                6.71
## 1117           7.1               8.3         60.3175                1.15
## 1146           2.1               2.6         73.3560               11.49
## 1150          13.4              15.5        132.2455                3.27
## 1157           3.3               4.1         71.7100               10.36
## 1158          67.6              93.2        328.8035                8.11
## 1164          13.0              14.0         99.0935                9.68
## 1197           2.0               2.7         53.5860                8.55
## 1205          10.0              11.4         97.1970                3.57
## 1206          20.2              23.5         70.9135                0.39
## 1225           5.1               6.2        110.5150               10.27
## 1227          34.7              49.4        190.0275                0.19
## 1251          19.5              21.9        136.3935                9.23
## 1262          13.4              15.5        140.0675                4.16
## 1266          32.6              37.5        134.7150                0.92
## 1306           3.0               3.7         64.6875               11.60
## 1320          13.6              15.8        171.2775                6.76
## 1338          37.6              52.6        262.2240                2.05
## 1358          33.3              47.6        315.4730                2.63
## 1481          42.1              61.3        368.1410                3.84
## 1492           5.7               6.6         51.8135                7.37
## 1503          35.2              48.9        223.6080                1.65
## 1531           3.3               4.0        100.8610                8.49
## 1536           3.8               4.4         70.7555                6.68
## 1559          25.4              31.3        184.5200                3.15
## 1566           3.2               3.7         61.0195               10.81
## 1588           4.2               4.9         90.2285                9.64
## 1604          19.9              22.3        165.7935                5.37
## 1614           3.7               4.3         49.3840                9.62
## 1620          23.7              28.3        163.8125                1.65
## 1624           6.7               7.8         56.2695                1.03
## 1629          55.0              82.7        203.5835                0.00
## 1707          46.1              60.7        221.5195                0.03
## 1710          46.9              67.7        302.8220                3.50
## 1713          10.6              11.9        182.1110                3.33
## 1716           5.4               6.3        114.3280                7.20
## 1722          19.0              22.3        145.3510                5.21
## 1732          24.2              28.9        164.8710                1.59
## 1785           5.4               6.3         96.0670                4.90
## 1801           8.8              10.6         88.0930                0.67
## 1810           3.8               4.5         69.3335                9.59
## 1820          51.8              93.8        249.0860                0.12
## 1824          12.6              14.1        125.4875                4.04
## 1844          31.0              38.1        129.7530                0.01
## 1875          83.6             134.3        308.3030                0.00
## 1882          17.3              19.3        140.8150                2.59
## 1905           7.6               8.9        105.6850                6.00
## 1948           6.7               7.9         88.8665                7.89
## 1950           3.3               3.9         71.3120               11.06
## 1976          64.4              88.3        241.0125                3.18
## 1984           3.5               4.1         67.1710                9.42
## 1989          34.6              47.7        203.5740                6.31
## 2022          12.8              14.5        144.3615                2.83
## 2077          40.2              51.0        225.4075                1.36
## 2081           2.2               2.7         50.9615                1.82
## 2118          13.3              15.5         81.8615                0.01
## 2120           4.2               4.9        113.6690               10.47
## 2127           3.0               3.5         52.9595                7.14
## 2128           4.5               5.7         89.2395                4.65
## 2146          12.2              15.7        124.0700                5.68
## 2148          23.6              28.2        131.2085                1.42
## 2178          27.3              31.8        175.6540                3.34
## 2182           4.2               5.1        131.7765               10.95
## 2235          87.9             123.3        411.0745                0.90
## 2279           3.3               3.9         61.7325                9.68
## 2281          19.8              23.3        149.5290                0.18
## 2291           9.4              10.5        156.2355                6.95
## 2322          12.0              14.0        158.5890                9.27
## 2324          18.2              20.3        170.1290                4.75
## 2325           2.3               2.8         54.3930               11.37
## 2339          11.4              13.3        134.7895                0.01
## 2357           5.8               6.8        107.3770                8.78
## 2368          10.2              11.5        117.1895                8.49
## 2379          27.4              33.1        208.0030                0.04
## 2396           2.4               2.9         51.6435                9.59
## 2405          16.7              19.5        125.1490                4.54
## 2410          42.1              53.8        195.6250                7.09
## 2443           1.8               2.3         55.3590                7.66
## 2449          50.8              75.9        271.7090                1.36
## 2469           2.4               3.1        116.3510               16.72
## 2496          23.4              29.6        199.7365                4.52
## 2519           7.7               9.2        128.6030                9.45
## 2526          52.8              69.9        243.6235                2.78
## 2582          65.7              90.8        396.4580                1.54
## 2618          59.6             100.9        257.9580                7.03
## 2621          13.2              15.4        123.9060                3.69
## 2642          42.8              50.2        149.7365                0.41
## 2651          20.6              24.4        185.8580                2.63
## 2662          66.8             108.3        267.5905                0.62
## 2680          15.9              18.6        111.9490                2.10
## 2702           7.5               8.7        109.1795                2.72
## 2711          43.2              62.4        224.4230                0.76
## 2713           3.2               4.2         75.4835               11.87
## 2728           6.9               8.1        121.7230                0.55
## 2738          10.7              12.4        134.0135                0.23
## 2753          28.6              36.3        351.3925                7.20
## 2754          14.8              17.2         91.3430                1.50
## 2821          16.4              19.1        141.5540                6.21
## 2841          54.6              65.8        251.7490                0.32
## 2847          16.6              19.4        148.4805                3.72
## 2849           6.5               7.6         66.6840                1.53
##      Hepatitis_B Measles  BMI Polio Diphtheria Incidents_HIV GDP_per_capita
## 1             97      65 27.8    97         97          0.08          11006
## 2             97      94 26.0    97         97          0.09          25742
## 7             97      97 26.2    97         97          0.08           9313
## 28            84      64 24.3    77         84          1.12           1383
## 44            97      64 23.9    96         97          0.96            661
## 58            95      99 25.5    95         95          0.05           4178
## 75            99      98 26.3    99         99          0.05          18445
## 102           69      64 21.3    68         69          0.24            467
## 111           88      91 26.6    95         95          0.04          74356
## 113           97      65 21.7    97         97          0.12           2582
## 122           90      83 26.8    84         90         14.30           3680
## 161           95      80 24.3    96         95          5.81           6403
## 167           94      92 26.6    94         95          0.29          13786
## 174           91      65 22.4    90         91          0.17            902
## 183           81      64 21.9    78         81          0.35            497
## 203           99      99 26.6    99         99          0.22           5967
## 217           64      64 23.2    62         64          0.89           3128
## 220           22      57 26.5    51         23          0.23           2125
## 242           92      90 27.3    92         92          0.19          11643
## 269           96      97 27.2    95         95          0.08          35808
## 272           92      87 28.0    92         92          0.03          38631
## 301           46      64 21.9    52         46          0.42            776
## 304           98      65 26.2    85         98          0.17           2167
## 331           56      76 28.6    72         58          0.13           4688
## 334           87      64 23.4    83         87          1.58            603
## 416           97      83 26.7    98         97          0.07           2302
## 427           54      64 22.9    47         54          0.74            769
## 444           67      95 26.0    98         98          0.08          51545
## 452           78      31 23.0    85         78          0.15           3332
## 474           81      83 26.4    87         85          0.38           6922
## 488           82      96 27.9    87         87          0.16           9617
## 496           97      99 27.0    97         97          0.08          17830
## 499           82      83 23.5    72         82          0.33           1077
## 512           98      83 27.1    97         98          0.40           7207
## 547           82      76 30.0    80         78          0.17           1535
## 557           96      80 26.5    98         96          0.24           8814
## 559           95      95 26.3    92         95          0.59           5577
## 580           99      99 23.7    99         99          0.10           8016
## 585           95      88 20.7    95         95          0.10           9011
## 591           99      96 29.5    99         99          0.13          29870
## 599           55      86 26.9    91         91          0.10          43596
## 609           92      89 26.9    99         92          0.40           9097
## 627           99      98 26.6    99         99          0.03           3953
## 629           93      82 24.9    85         93         10.00           1146
## 639           98      96 28.4    97         98          0.13          20628
## 640           87      69 21.7    86         87          0.06           1606
## 651           94      92 26.4    93         93          0.09          14264
## 688           99      99 26.4    99         99          0.08           6433
## 697           99      84 26.6    86         99          0.20          14285
## 700           88      64 22.8    88         88          2.59            381
## 717           89      78 22.6    89         89          0.28           1197
## 728           98      98 26.6    97         97          3.50          15158
## 733           94      92 25.5    95         95          0.04          45193
## 741           94      65 21.6    94         94          0.27            306
## 764           88      64 22.7    88         80          3.50            590
## 766           92      87 26.4    91         91          0.03           7075
## 770           86      60 22.7    86         86          0.85            588
## 787           41      47 28.2    50         41          0.13            979
## 810           91      88 27.6    92         91          0.18           3706
## 811           73      92 26.8    72         73          0.40          13630
## 833           99      96 28.9    99         99          0.13           4164
## 838           98      64 23.1    96         98          2.01            948
## 840           80      64 25.2    79         80          1.09           7385
## 850           96      98 26.9    98         96          0.05           5500
## 852           49      64 23.2    42         49          0.58           2687
## 853           99      95 24.3    99         99          0.16           5840
## 869           99      98 26.1    99         99          0.01           3875
## 874           98      95 25.7    98         98          0.12          19250
## 901           99      99 25.3    99         99          0.17           9033
## 903           91      64 24.3    92         91          0.01           1243
## 904           90      79 27.5    88         96          0.40          18384
## 907           99      99 28.4    99         99          0.13          38663
## 957           78      64 22.4    85         78          2.08            847
## 1000          96      76 24.7    96         96          0.15           1585
## 1011          72      54 23.9    72         72          0.13           1357
## 1058          88      63 23.9    88         88          0.84           1774
## 1064          88      92 25.9    97         97          0.08          42802
## 1067          65      42 23.3    67         65          0.03            556
## 1068          94      95 28.9    94         94          0.40           4805
## 1117          81      63 27.5    81         81          0.04           7643
## 1146          88      96 26.5    95         95          0.01          20890
## 1150          91      83 27.6    91         91          0.47           4908
## 1157          98      85 26.1    99         99          0.08          41008
## 1158          40      64 23.9    37         16          4.20          11283
## 1164          97      89 27.7    97         97          0.28          16559
## 1197          83      93 22.7    99         96          0.17          34961
## 1205          92      97 26.7    92         91          0.08           4862
## 1206          99      95 25.9    99         99          0.03           2875
## 1225          96      97 26.4    96         96          0.02          16342
## 1227          89      54 22.9    85         89          0.10           1219
## 1251          99      83 29.8    99         99          0.40          10094
## 1262          91      86 26.1    91         91          0.19           6176
## 1266          96      94 25.9    96         96          0.11            978
## 1306          93      88 25.5    93         93          0.08          44196
## 1320          88      92 27.0    88         87          0.36           2732
## 1338          80      64 23.1    80         80          2.04           2449
## 1358          92      64 24.2    92         92          4.58           4897
## 1481          87      64 23.8    88         87          3.86           1445
## 1492          95      91 27.1    97         97          0.08          24922
## 1503          89      28 23.3    83         89          1.15           1465
## 1531          82      94 26.5    89         89          0.03           6517
## 1536          96      83 27.1    99         99          0.06          18084
## 1559          99      83 26.4    99         99          0.15           3036
## 1566          95      86 27.4    95         95          0.07          62012
## 1588          94      96 27.3    94         94          0.02          11933
## 1604          97      65 26.5    97         97          0.12           1121
## 1614          88      87 25.2    96         97          0.05          84776
## 1620          74      83 26.5    69         74          0.03           3995
## 1624          99      91 29.1    99         99          0.06          63039
## 1629          73      64 24.9    67         73          0.15           1524
## 1707          69      95 23.7    63         69          0.03           1602
## 1710          90      47 22.5    90         90          4.48           1338
## 1713          98      98 26.3    98         98          0.14          10511
## 1716          94      86 26.0    95         95          0.02           5589
## 1722          93      72 26.6    93         93          0.14           5414
## 1732          78      65 29.6    71         72          0.17           2907
## 1785          82      88 25.7    74         82          0.08           4730
## 1801          99      97 27.0    99         99          0.10          31164
## 1810          88      86 27.1    96         96          0.08          45405
## 1820          65      64 21.8    83         65          0.06            484
## 1824          94      97 26.3    96         94          0.09           3607
## 1844          97      90 21.6    98         97          0.01           1248
## 1875          42      64 23.1    47         42          0.13            386
## 1882          99      99 26.7    99         99          0.14           2754
## 1905          95      93 27.3    95         95          0.24          15614
## 1948          97      89 27.9    96         96          0.19          13495
## 1950          88      93 26.5    92         95          0.03          41103
## 1976          52      64 24.0    65         52          3.50            722
## 1984          88      80 25.3    93         93          0.03          53255
## 1989          98      87 22.0    99         98          0.59            751
## 2022          97      96 25.2    98         97          0.70           9260
## 2077          67      65 25.5    51         73          0.41           2679
## 2081          96      90 23.6    96         96          0.07          55647
## 2118          98      65 26.1    98         98          0.04           5201
## 2120          96      94 26.6    92         98          0.08          12578
## 2127          93      83 25.6    93         93          0.06          30242
## 2128          99      99 25.6    99         99          0.16           7694
## 2146          90      63 26.5    88         90          0.13           6229
## 2148          64      65 26.1    80         64          0.17           2696
## 2178          89      61 22.1    92         89          0.10           1163
## 2182          88      99 27.2    99         99          0.08          12721
## 2235          47      64 22.8    51         47          1.12            377
## 2279          93      93 27.1    93         93          0.04          56707
## 2281          93      64 29.5    93         93          0.13           3563
## 2291          94      91 27.5    91         94          0.14           4014
## 2322          95      83 27.9    95         95          0.34          31699
## 2324          89      21 26.5    78         89          0.47           9168
## 2325          94      86 26.3    99         99          0.10         105462
## 2339          97      97 28.0    97         97          0.08           7590
## 2357          92      86 28.8    93         95          0.12          56763
## 2368          94      87 27.6    93         94          0.13          13789
## 2379          99      94 23.8    98         99          0.13           2753
## 2396          97      88 26.8    97         97          0.06          23408
## 2405          96      95 24.5    93         93          0.26           3043
## 2410          89      65 22.8    89         89          0.15           2140
## 2443          88      94 26.2    92         92          0.05          52952
## 2449          88      64 23.5    82         88          0.72            571
## 2469          91      92 26.4    93         93          0.08          17402
## 2496          75      57 23.1    79         60          0.10           3001
## 2519          90      80 26.7    89         89          0.04           8969
## 2526          64      83 25.2    64         60          0.67           1387
## 2582          83      64 23.7    81         83          0.63           1973
## 2618          91      50 22.1    91         91          0.16            653
## 2621          78      76 27.1    84         78          0.16           6124
## 2642          76      64 21.2    75         76          0.10           1333
## 2651          99      94 27.6    99         99          0.12           5391
## 2662          64      64 22.9    67         64          0.39            751
## 2680          59      55 32.1    78         66          0.17           4074
## 2702          99      99 23.0    99         99          0.01           3844
## 2711          77      64 20.5    75         77          0.19            641
## 2713          86      79 25.0    97         98          0.09          36653
## 2728          99      99 25.6    99         99          0.14           9955
## 2738          78      99 32.1    96         78          0.17           4336
## 2753          75      59 27.2    85         75          6.91           6260
## 2754          98      98 26.3    98         98          0.04           4095
## 2821          87      83 26.7    87         87          0.40          17318
## 2841          84      82 24.0    84         84          0.22           2653
## 2847          98      83 27.2    99         98          0.11           2050
## 2849          98      99 24.8    98         98          0.05          22634
##      Population_mln Thinness_ten_nineteen_years Thinness_five_nine_years
## 1             78.53                         4.9                      4.8
## 2             46.44                         0.6                      0.5
## 7            144.10                         2.3                      2.3
## 28            23.30                         5.6                      5.5
## 44             2.09                         7.3                      7.2
## 58            39.73                         6.0                      5.8
## 75             4.27                         7.1                      6.9
## 102           24.23                         7.1                      7.1
## 111            5.19                         0.8                      0.7
## 113           92.68                        14.2                     14.5
## 122            1.10                         4.0                      4.1
## 161            2.12                         6.4                      6.1
## 167            1.98                         2.2                      2.1
## 174           27.02                        15.7                     16.1
## 183           76.24                         9.5                      9.3
## 203            9.46                         1.9                      2.0
## 217           27.88                         8.3                      8.2
## 220           45.15                         2.3                      2.4
## 242            4.85                         1.7                      1.7
## 269            8.38                         1.2                      1.1
## 272            4.61                         0.4                      0.3
## 301           14.11                         8.5                      8.4
## 304            0.60                         1.1                      1.2
## 331           35.57                         5.3                      5.1
## 334            1.74                         7.1                      7.0
## 416            9.11                         2.1                      2.1
## 427           11.43                         7.3                      7.3
## 444            9.80                         1.5                      1.4
## 452          258.38                         1.4                      1.2
## 474           10.28                         3.3                      3.2
## 488          121.86                         1.5                      1.5
## 496           10.55                         1.8                      1.8
## 499           10.58                         6.9                      6.8
## 512            0.11                         3.5                      3.4
## 547            0.11                         0.1                      0.1
## 557          204.47                         2.7                      2.6
## 559            0.77                         5.5                      5.3
## 580         1379.86                         3.6                      2.9
## 585            0.35                         8.4                      8.2
## 591            3.84                         3.5                      3.4
## 599           35.70                         0.6                      0.5
## 609            0.11                         3.8                      3.8
## 627            2.88                         1.2                      1.3
## 629            2.06                         5.5                      5.3
## 639           31.72                         7.8                      7.6
## 640         1310.15                        26.7                     27.3
## 651            2.90                         2.6                      2.6
## 688            5.57                         3.3                      3.3
## 697            0.09                         3.3                      3.3
## 700           16.75                         6.4                      6.2
## 717           52.68                        12.8                     13.0
## 728            0.09                         5.7                      6.0
## 733           16.94                         1.0                      0.9
## 741           10.16                         7.3                      7.2
## 764           27.04                         3.6                      3.5
## 766            7.18                         1.9                      1.8
## 770            7.17                         7.4                      7.3
## 787           18.00                         6.3                      6.1
## 810            6.33                         1.6                      1.5
## 811            3.97                         1.9                      1.8
## 833            9.27                         4.0                      4.0
## 838           51.48                         6.7                      6.5
## 840            1.95                         6.1                      5.9
## 850            9.65                         2.8                      2.9
## 852          181.14                         9.8                      9.7
## 853           68.71                         7.7                      7.7
## 869            3.00                         2.2                      2.3
## 874           10.36                         0.7                      0.5
## 901            0.45                        13.6                     13.6
## 903            0.78                         6.7                      6.5
## 904            1.37                         5.7                      5.9
## 907            9.26                         5.3                      5.1
## 957           38.23                         5.6                      5.6
## 1000           0.20                         5.5                      5.3
## 1011         199.43                        19.2                     19.6
## 1058          27.85                         6.2                      6.1
## 1064           5.48                         0.9                      0.8
## 1067          34.41                        17.2                     17.3
## 1068           0.36                         3.5                      3.4
## 1117           6.53                         4.9                      4.9
## 1146           2.06                         1.4                      1.3
## 1150           2.89                         1.8                      1.7
## 1157          11.27                         1.0                      1.0
## 1158           1.17                         8.4                      8.3
## 1164           0.29                         3.8                      3.7
## 1197         127.14                         2.1                      1.8
## 1205           2.07                         2.1                      2.1
## 1206          34.66                         6.4                      6.2
## 1225           5.42                         1.2                      1.2
## 1227          14.58                         9.5                      9.3
## 1251           0.18                         4.3                      4.3
## 1262          47.52                         2.1                      1.9
## 1266           8.45                         3.6                      3.7
## 1306           8.64                         1.9                      2.1
## 1320           2.83                         2.7                      2.8
## 1338           4.86                         7.5                      7.1
## 1358           2.31                         8.2                      8.1
## 1481          13.81                         5.6                      5.5
## 1492           0.45                         0.8                      0.8
## 1503          47.88                         7.8                      7.6
## 1531           0.62                         1.8                      1.8
## 1536          10.82                         0.8                      0.7
## 1559          10.87                         1.2                      1.1
## 1566           4.70                         0.3                      0.2
## 1588           4.20                         1.5                      1.4
## 1604           5.96                         3.3                      3.4
## 1614           8.28                         0.4                      0.3
## 1620          15.57                         1.2                      1.2
## 1624           2.57                         5.2                      4.9
## 1629           4.05                         7.8                      7.5
## 1707          26.50                        13.6                     13.4
## 1710          15.88                         6.3                      6.1
## 1713          17.54                         2.4                      2.5
## 1716           7.10                         2.0                      2.0
## 1722           6.69                         2.0                      1.9
## 1732           0.11                         0.2                      0.2
## 1785           3.43                         2.3                      2.3
## 1801           0.41                         5.7                      5.1
## 1810          65.12                         0.8                      0.6
## 1820          20.00                         9.6                      9.4
## 1824           2.93                         2.1                      2.2
## 1844         156.26                        17.9                     18.3
## 1875          13.80                         6.6                      6.4
## 1882          31.30                         3.0                      3.1
## 1905           3.41                         1.5                      1.4
## 1948          17.97                         0.8                      0.8
## 1950          81.69                         1.1                      1.1
## 1976           4.47                         6.5                      6.4
## 1984           5.68                         1.1                      0.9
## 1989          11.37                         5.7                      5.7
## 2022           1.26                         6.9                      6.8
## 2077           8.11                         1.3                      1.3
## 2081           5.54                         2.2                      2.2
## 2118          78.49                         8.5                      8.6
## 2120          37.99                         1.9                      2.0
## 2127          60.73                         0.6                      0.6
## 2128          11.32                         3.5                      3.3
## 2146          30.47                         1.1                      1.1
## 2148           0.27                         1.5                      1.4
## 2178          15.52                         1.9                      1.9
## 2182           9.84                         1.6                      1.6
## 2235           4.49                         8.2                      8.2
## 2279          23.82                         0.6                      0.6
## 2281          92.44                         2.8                      2.8
## 2291           3.73                         2.7                      2.8
## 2322           0.37                         2.5                      2.5
## 2324           0.56                         3.5                      3.5
## 2325           0.57                         1.0                      0.9
## 2339           6.42                         5.8                      5.5
## 2357         320.74                         0.8                      0.6
## 2368          43.13                         1.0                      0.9
## 2379           0.73                        15.4                     16.0
## 2396           1.16                         1.0                      1.0
## 2405           0.52                         6.6                      6.6
## 2410           6.74                         8.8                      8.9
## 2443           0.33                         1.0                      0.9
## 2449           7.32                         6.5                      6.2
## 2469           1.32                         1.9                      1.9
## 2496         102.11                         1.0                      9.7
## 2519          19.82                         2.5                      2.7
## 2526          10.70                         3.9                      3.9
## 2582          23.23                         5.5                      5.5
## 2618          18.11                         8.0                      7.5
## 2621          16.21                         1.2                      1.1
## 2642           1.20                         1.9                     11.1
## 2651           0.87                         4.0                      3.7
## 2662          17.44                         7.7                      7.5
## 2680           0.19                         0.2                      0.1
## 2702          20.97                        15.1                     15.0
## 2711         100.84                         1.4                      1.2
## 2713          66.55                         0.7                      0.6
## 2728          30.27                         7.5                      7.3
## 2738           0.10                         0.1                      0.1
## 2753          55.39                         4.4                      5.3
## 2754          11.18                         6.5                      6.4
## 2821          30.08                         1.6                      1.5
## 2841           0.91                         5.6                      5.4
## 2847           6.22                         1.8                      1.7
## 2849           1.37                         6.2                      6.1
##      Schooling Life_expectancy
## 1          7.8            76.5
## 2          9.7            82.8
## 7         12.0            71.2
## 28         6.1            57.6
## 44         3.4            60.9
## 58         7.9            76.1
## 75         9.5            76.9
## 102        6.1            65.5
## 111       12.5            82.3
## 113        8.0            75.1
## 122        6.5            55.4
## 161        9.2            67.3
## 167       12.8            74.5
## 174        4.7            69.5
## 183        6.4            59.3
## 203       12.2            73.6
## 217        5.0            59.4
## 220       11.3            71.2
## 242        8.8            79.6
## 269       13.0            82.1
## 272       12.4            81.5
## 301        2.3            53.1
## 304        5.4            72.2
## 331        6.6            69.9
## 334        2.9            57.0
## 416        6.3            74.5
## 427        2.6            59.6
## 444       12.4            82.2
## 452        7.9            70.8
## 474        7.8            73.2
## 488        8.6            74.9
## 496       12.7            78.6
## 499        3.5            60.6
## 512        8.6            72.1
## 547        7.9            67.3
## 557        7.6            75.0
## 559        8.4            69.3
## 580        7.7            75.9
## 585        3.9            64.7
## 591        7.1            75.1
## 599       13.1            81.9
## 609        8.7            72.4
## 627        9.7            78.0
## 629        6.1            51.0
## 639        9.5            74.7
## 640        6.3            68.6
## 651       13.0            74.3
## 688        9.8            67.7
## 697        9.2            76.5
## 700        4.4            62.0
## 717        4.9            65.8
## 728        9.5            74.3
## 733       12.1            81.5
## 741        2.9            60.1
## 764        3.5            57.2
## 766       11.8            74.6
## 770        3.4            52.9
## 787        5.1            69.9
## 810        6.6            72.4
## 811        9.9            77.8
## 833       10.3            74.1
## 838        5.8            63.1
## 840        8.1            64.9
## 850       10.7            72.3
## 852        6.0            53.1
## 853        7.6            76.1
## 869       10.1            69.1
## 874        9.1            81.1
## 901        6.3            77.7
## 903        4.8            63.5
## 904       10.8            72.9
## 907       10.6            77.3
## 957        5.7            61.4
## 1000       5.6            69.4
## 1011       5.1            66.6
## 1058       6.9            62.8
## 1064      12.4            81.5
## 1067       3.6            63.4
## 1068      10.5            74.0
## 1117       8.5            78.8
## 1146      12.0            80.8
## 1150       9.6            74.1
## 1157      11.7            81.0
## 1158       5.5            57.4
## 1164      10.5            78.8
## 1197      12.5            83.8
## 1205       9.6            75.4
## 1206       5.0            75.7
## 1225      12.5            76.6
## 1227       2.9            66.7
## 1251       8.9            75.6
## 1262       8.1            76.5
## 1266      10.5            70.1
## 1306      12.1            81.2
## 1320      11.6            71.5
## 1338       6.3            63.1
## 1358       6.7            62.1
## 1481       8.2            59.5
## 1492      11.2            81.9
## 1503       6.3            64.8
## 1531      11.3            76.4
## 1536      10.6            81.0
## 1559       8.7            70.3
## 1566      12.3            81.5
## 1588      11.2            77.3
## 1604      10.8            70.7
## 1614      13.4            82.9
## 1620       6.3            73.3
## 1624       9.8            79.8
## 1629       4.3            63.9
## 1707       3.0            66.1
## 1710       6.9            61.7
## 1713      11.7            72.0
## 1716      11.0            75.3
## 1722       8.5            73.7
## 1732       8.0            67.3
## 1785       9.0            76.9
## 1801       9.0            75.3
## 1810      12.8            81.0
## 1820       1.8            60.6
## 1824      11.6            74.5
## 1844       5.2            71.5
## 1875       2.1            55.9
## 1882      11.4            70.9
## 1905       8.7            77.4
## 1948      10.3            79.6
## 1950      14.1            80.6
## 1976       4.4            62.3
## 1984      12.5            80.7
## 1989       4.0            67.5
## 2022       9.1            74.4
## 2077       4.3            63.5
## 2081      11.5            82.7
## 2118       9.8            75.8
## 2120      12.1            77.5
## 2127      10.2            82.5
## 2128      11.4            78.6
## 2146       9.1            75.8
## 2148       6.8            69.9
## 2178       4.7            68.6
## 2182      11.8            75.6
## 2235       4.2            50.9
## 2279      12.8            82.4
## 2281       7.1            71.3
## 2291      12.7            73.0
## 2322      11.1            73.1
## 2324       8.4            71.2
## 2325      12.0            82.3
## 2339       7.3            72.1
## 2357      13.3            78.7
## 2368       9.8            76.1
## 2379       3.1            70.4
## 2396      11.9            80.4
## 2405       5.9            72.1
## 2410       5.1            66.5
## 2443      12.2            82.5
## 2449       4.7            59.9
## 2469      12.7            77.6
## 2496       9.3            70.6
## 2519      10.9            74.9
## 2526       5.2            62.5
## 2582       5.0            56.1
## 2618       1.4            59.9
## 2621       8.4            76.1
## 2642       4.5            68.5
## 2651      10.8            67.1
## 2662       2.3            57.5
## 2680      10.3            72.7
## 2702      10.9            76.3
## 2711       2.6            65.0
## 2713      11.5            82.3
## 2728      10.2            75.5
## 2738      11.2            70.5
## 2753      10.1            62.6
## 2754       7.0            75.9
## 2821      10.1            72.6
## 2841       4.1            64.1
## 2847       6.5            73.6
## 2849       9.3            76.8
cm <- cor(data2, method="pearson")
corrplot::corrplot(cm, method= "number", order = "hclust")

KMO(r=cm)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = cm)
## Overall MSA =  0.84
## MSA for each item = 
##               Infant_deaths           Under_five_deaths 
##                        0.86                        0.83 
##             Adult_mortality         Alcohol_consumption 
##                        0.84                        0.83 
##                 Hepatitis_B                     Measles 
##                        0.82                        0.97 
##                         BMI                       Polio 
##                        0.87                        0.93 
##                  Diphtheria               Incidents_HIV 
##                        0.80                        0.70 
##              GDP_per_capita              Population_mln 
##                        0.88                        0.85 
## Thinness_ten_nineteen_years    Thinness_five_nine_years 
##                        0.73                        0.72 
##                   Schooling             Life_expectancy 
##                        0.92                        0.87
print(cortest.bartlett(cm,nrow(data2)))
## $chisq
## [1] 3781.936
## 
## $p.value
## [1] 0
## 
## $df
## [1] 120
parallel <- fa.parallel(data2, fm = "minres", fa = "fa")

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA
factanal(data2, factors = 3, ,lower=0.01225)$PVAL
##    objective 
## 9.683779e-78
factanal(data2, factors =7,lower=0.0122222225 )$PVAL
##    objective 
## 0.0002878897
f<-factanal(data2, factors = 7,lower=0.0122222225)
f
## 
## Call:
## factanal(x = data2, factors = 7, lower = 0.0122222225)
## 
## Uniquenesses:
##               Infant_deaths           Under_five_deaths 
##                       0.012                       0.012 
##             Adult_mortality         Alcohol_consumption 
##                       0.012                       0.421 
##                 Hepatitis_B                     Measles 
##                       0.072                       0.554 
##                         BMI                       Polio 
##                       0.012                       0.103 
##                  Diphtheria               Incidents_HIV 
##                       0.016                       0.478 
##              GDP_per_capita              Population_mln 
##                       0.348                       0.871 
## Thinness_ten_nineteen_years    Thinness_five_nine_years 
##                       0.012                       0.012 
##                   Schooling             Life_expectancy 
##                       0.173                       0.021 
## 
## Loadings:
##                             Factor1 Factor2 Factor3 Factor4 Factor5 Factor6
## Infant_deaths               -0.418  -0.433   0.433   0.146  -0.297   0.574 
## Under_five_deaths           -0.440  -0.402   0.414   0.132  -0.320   0.586 
## Adult_mortality             -0.301  -0.373   0.796          -0.245   0.249 
## Alcohol_consumption          0.151   0.680          -0.229          -0.190 
## Hepatitis_B                  0.955                                         
## Measles                      0.443   0.329  -0.224           0.262  -0.123 
## BMI                          0.133   0.149  -0.159  -0.409   0.855  -0.157 
## Polio                        0.893   0.204  -0.144                  -0.166 
## Diphtheria                   0.965   0.181  -0.117                         
## Incidents_HIV                                0.721                         
## GDP_per_capita               0.133   0.724  -0.297  -0.112                 
## Population_mln                                       0.342                 
## Thinness_ten_nineteen_years         -0.315   0.134   0.903           0.201 
## Thinness_five_nine_years            -0.323   0.125   0.896  -0.131   0.154 
## Schooling                    0.268   0.657  -0.174  -0.241   0.343  -0.339 
## Life_expectancy              0.349   0.524  -0.623           0.243  -0.353 
##                             Factor7
## Infant_deaths                      
## Under_five_deaths                  
## Adult_mortality                    
## Alcohol_consumption                
## Hepatitis_B                        
## Measles                            
## BMI                                
## Polio                              
## Diphtheria                         
## Incidents_HIV                      
## GDP_per_capita                     
## Population_mln                     
## Thinness_ten_nineteen_years        
## Thinness_five_nine_years     0.122 
## Schooling                          
## Life_expectancy                    
## 
##                Factor1 Factor2 Factor3 Factor4 Factor5 Factor6 Factor7
## SS loadings      3.564   2.592   2.175   2.086   1.277   1.157   0.025
## Proportion Var   0.223   0.162   0.136   0.130   0.080   0.072   0.002
## Cumulative Var   0.223   0.385   0.521   0.651   0.731   0.803   0.805
## 
## Test of the hypothesis that 7 factors are sufficient.
## The chi square statistic is 62.63 on 29 degrees of freedom.
## The p-value is 0.000288
load <- f$loadings[,1:2]
plot(load,type="n") # set up plot
text(load,labels=names(data2),cex=.7)

names(f$loadings[,1])[abs(f$loadings[,1])>0.4]
## [1] "Infant_deaths"     "Under_five_deaths" "Hepatitis_B"      
## [4] "Measles"           "Polio"             "Diphtheria"
f1<-data2[,names(f$loadings[,1])[abs(f$loadings[,1])>0.4]]
summary(alpha(f1, check.keys=TRUE))
## Number of categories should be increased  in order to count frequencies.
## Warning in alpha(f1, check.keys = TRUE): Some items were negatively correlated with the first principal component and were automatically reversed.
##  This is indicated by a negative sign for the variable name.
## 
## Reliability analysis   
##  raw_alpha std.alpha G6(smc) average_r S/N   ase mean sd median_r
##       0.89      0.92    0.96      0.67  12 0.011   95 16     0.59
scores<-factanal(data2, factors = 7,lower=0.0122222225,scores="regression")$scores
head(scores)
##         Factor1    Factor2   Factor3    Factor4     Factor5     Factor6
## 1   0.638322681 -0.6669749 -0.583670  0.1180494  1.09915803 -0.03638192
## 2   0.380428326  1.0250218 -1.001402 -0.5856033 -0.48752162 -0.01020663
## 7   0.658902252  0.4200210  1.672434 -0.3090451  0.02366873 -1.58966325
## 28 -0.001745963 -0.3580919  1.777462 -0.3923677 -0.27800581  1.23305421
## 44  1.010716464 -1.4200139  0.841323  0.0809353 -0.58536651  0.24317847
## 58  0.507667521 -0.3947061 -1.120713  0.3166194 -0.01042125  0.52130319
##         Factor7
## 1   0.023789785
## 2  -0.002407151
## 7  -0.342100665
## 28 -0.193267846
## 44 -0.452529575
## 58  0.109165559
cm <- cor(data2, method="pearson")
corrplot::corrplot(cm, method= "number", order = "hclust")